Maxim Dolgolyov
a07e631e8e
- 020_algebra_9_hub.sql: hub (slug 'algebra-9', indigo, 19 параграфов) + 4 главы - algebra_9_hub.html: страница каталога с индиго-палитрой - algebra_9_ch1..ch4.html: skeleton-страницы 4 глав * Глава 1 (amber): §1-§5 Рациональные выражения * Глава 2 (emerald): §6-§9 Функции * Глава 3 (violet): §10-§13 Дробно-рациональные уравнения и неравенства * Глава 4 (cyan): §14-§19 Прогрессии - Все skeleton-файлы рабочие: переключение параграфов, theme toggle, search modal, sidebar, progress, XP. Stub-плейсхолдеры в buildPx(). - Наполнение параграфов запланировано на Phase 1+.
574 lines
41 KiB
HTML
574 lines
41 KiB
HTML
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<title>Алгебра 9 · Глава 3 · Дробно-рациональные уравнения и неравенства</title>
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</head>
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<body>
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<header class="hdr">
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<div class="hdr-row">
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<div>
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<h1>Алгебра 9 · Глава 3</h1>
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<div class="hdr-sub">Уравнения · системы · окружность · метод интервалов</div>
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</div>
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<div class="hdr-side">
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<a href="/textbook/algebra-9" class="hdr-btn"><svg class="ic" viewBox="0 0 24 24"><polyline points="15 18 9 12 15 6"/></svg> К алгебре 9</a>
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<button id="search-btn" class="hdr-btn"><svg class="ic" viewBox="0 0 24 24"><circle cx="11" cy="11" r="7"/><path d="m21 21-4-4"/></svg> Поиск</button>
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<button id="theme-btn" class="hdr-btn"><svg class="ic" viewBox="0 0 24 24"><path d="M21 12.8A9 9 0 1 1 11.2 3a7 7 0 0 0 9.8 9.8z"/></svg><span id="theme-lab">Тёмная</span></button>
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</div>
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</div>
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</header>
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<main class="main">
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<div class="col-main">
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<section class="hero">
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||
<h2>Дробно-рациональные уравнения и неравенства</h2>
|
||
<p>Здесь мы изучаем <b>дробно-рациональные уравнения</b>, <b>системы нелинейных уравнений</b> (включая графический способ), <b>длину отрезка</b> и <b>уравнение окружности</b> $(x-a)^2 + (y-b)^2 = r^2$, а также <b>метод интервалов</b> для дробно-рациональных неравенств.</p>
|
||
<div class="hero-row">
|
||
<button class="btn-primary" onclick="goTo('p10')"><svg class="ic" viewBox="0 0 24 24"><polygon points="6 4 20 12 6 20 6 4" fill="currentColor" stroke="none"/></svg> Начать § 10</button>
|
||
<div class="hero-progress">
|
||
<span class="hp-label">Прогресс по главе</span>
|
||
<div class="hp-bar"><div id="hero-hp-fill" class="hp-fill"></div></div>
|
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<span id="hero-hp-text" class="hp-text">0%</span>
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</div>
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<div id="hero-xp-badge" class="hero-xp-badge"></div>
|
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</div>
|
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</section>
|
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<section class="psel">
|
||
<div class="psel-title">Параграфы главы</div>
|
||
<div id="psel-grid" class="psel-grid"></div>
|
||
</section>
|
||
|
||
<section id="sec-p10" class="sec" data-watermark="=0"><div class="sec-header"><span class="sec-num">§ 10</span><h2 class="sec-h">Дробно-рациональные уравнения</h2></div><div id="p10-body"></div></section>
|
||
<section id="sec-p11" class="sec" data-watermark="{"><div class="sec-header"><span class="sec-num">§ 11</span><h2 class="sec-h">Системы нелинейных уравнений</h2></div><div id="p11-body"></div></section>
|
||
<section id="sec-p12" class="sec" data-watermark="○"><div class="sec-header"><span class="sec-num">§ 12</span><h2 class="sec-h">Уравнение окружности</h2></div><div id="p12-body"></div></section>
|
||
<section id="sec-p13" class="sec" data-watermark=">0"><div class="sec-header"><span class="sec-num">§ 13</span><h2 class="sec-h">Метод интервалов</h2></div><div id="p13-body"></div></section>
|
||
<section id="sec-final3" class="sec" data-watermark="★"><div class="sec-header"><span class="sec-num" style="background:linear-gradient(135deg,#7c3aed,#a78bfa)">Финал главы</span><h2 class="sec-h">Итоги. 4 боссов главы 3</h2></div><div id="final3-body"></div></section>
|
||
|
||
</div>
|
||
<aside class="col-side" id="col-side"><div id="sidebar-content"></div></aside>
|
||
<div class="col-side-backdrop" id="col-side-backdrop"></div>
|
||
</main>
|
||
|
||
<footer class="foot">Интерактивный учебник «Алгебра 9» · Глава 3 · Дробно-рациональные уравнения и неравенства · LearnSpace</footer>
|
||
|
||
<div id="ach-popup" class="ach-popup"><svg class="ic" viewBox="0 0 24 24" style="width:22px;height:22px"><polygon points="12,2 22,20 2,20"/></svg><span id="ach-text">Достижение!</span></div>
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<div id="gloss-tip" class="gloss-tip"></div>
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<div id="search-modal" class="search-modal" role="dialog">
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<div class="search-box">
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<input type="text" id="search-input" class="search-input" placeholder="Поиск…" autocomplete="off">
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||
<div id="search-results" class="search-results"></div>
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||
<div class="search-foot"><span><kbd>↑↓</kbd> навигация</span><span><kbd>Enter</kbd> открыть</span><span><kbd>Esc</kbd> закрыть</span></div>
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|
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|
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{ id:'p10', num:'§ 10', name:'Дробно-рациональные уравнения', sub:'$\dfrac{P}{Q} = 0$' },
|
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|
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{ id:'p12', num:'§ 12', name:'Уравнение окружности', sub:'$(x-a)^2+(y-b)^2=r^2$' },
|
||
{ id:'p13', num:'§ 13', name:'Метод интервалов', sub:'неравенства' },
|
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{ id:'final3', num:'★', name:'Финал главы', sub:'Итоги · 4 боссов', final:true }
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|
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p10:{title:'Шпаргалка \xA710',rows:[['Дробно-рац. уравн.','$\dfrac{P(x)}{Q(x)} = 0$'],['Условие','$P(x) = 0$ и $Q(x) \ne 0$'],['Алгоритм','найди корни $P$ → проверь ОДЗ']]},
|
||
p11:{title:'Шпаргалка \xA711',rows:[['Система','несколько уравнений с общими $x, y$'],['Подстановка','выразил → подставил'],['Графически','точки пересечения графиков']]},
|
||
p12:{title:'Шпаргалка \xA712',rows:[['Длина','$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$'],['Окружность','$(x-a)^2 + (y-b)^2 = r^2$'],['Центр','$(a; b)$'],['Радиус','$r$']]},
|
||
p13:{title:'Шпаргалка \xA713',rows:[['Шаг 1','перенеси всё влево, приведи к виду $\dfrac{P}{Q}$'],['Шаг 2','найди нули $P$ и $Q$'],['Шаг 3','отметь на оси'],['Шаг 4','определи знаки']]},
|
||
final3:{title:'Финал главы',rows:[['§§10–13','теория главы 3'],['Боссов','4'],['Награда','+100 XP']]}
|
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|
||
|
||
const TIPS=[
|
||
{sec:'p10',html:'Дробно-рациональное уравнение $\dfrac{P(x)}{Q(x)} = 0$ равносильно системе: $P(x) = 0$ и $Q(x) \ne 0$.'},
|
||
{sec:'p11',html:'В системах нелинейных уравнений часто помогает <b>метод подстановки</b> или сложение.'},
|
||
{sec:'p12',html:'Длина отрезка: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Окружность: $(x - a)^2 + (y - b)^2 = r^2$.'},
|
||
{sec:'p13',html:'<b>Метод интервалов</b>: нули → точки на оси → знаки на промежутках.'},
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||
{sec:'final3',html:'4 босса главы 3.'}
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const xpPct=xpRange>0?Math.round(xpInLv/xpRange*100):100;
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html+='<div class="sidecard"><h4>'+sb.title+'</h4>';
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sb.rows.forEach(([k,v])=>{ html+='<div class="sidecard-row"><b>'+k+'</b>'+(v?' — '+v:'')+'</div>'; });
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function secNav(prev, next){
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const NAMES={p10:'\xA710',p11:'\xA711',p12:'\xA712',p13:'\xA713',final3:'Финал'};
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h+=next?'<button class="btn primary" onclick="goTo(\''+next+'\')">'+NAMES[next]+' <svg class="ic" viewBox="0 0 24 24"><polyline points="9 18 15 12 9 6"/></svg></button>':'<span></span>';
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+'<svg class="ic" viewBox="0 0 24 24"><path d="M4 19.5A2.5 2.5 0 0 1 6.5 17H20"/><path d="M6.5 2H20v20H6.5A2.5 2.5 0 0 1 4 19.5v-15A2.5 2.5 0 0 1 6.5 2z"/></svg>'
|
||
+' Я прочитал — '+(paraId.startsWith('final')?'финал':'\xA7'+paraId.replace('p',''))+' (+10 XP)'
|
||
+'</button></div>';
|
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}
|
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function wireReadBtn(paraId){
|
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const btn = document.getElementById(paraId+'-read-btn'); if(!btn) return;
|
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btn.addEventListener('click', ()=>{
|
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addXp(10, paraId+'-read'); bumpProgress(paraId, 100);
|
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btn.textContent='Прочитано! +10 XP'; btn.disabled=true; btn.style.opacity=.6;
|
||
if(paraId==='final3') achievement('ch3_done');
|
||
});
|
||
}
|
||
|
||
/* ===== STUB BUILDERS — наполнение в Phase 1+ ===== */
|
||
|
||
function buildP10(){
|
||
const root = document.getElementById('p10-body');
|
||
root.innerHTML = `
|
||
<div class="card">
|
||
<div class="card-header">
|
||
<span class="card-icon theory">${ICONS.theory}</span>
|
||
<span class="card-title">В разработке</span>
|
||
<span class="card-num">§ 10</span>
|
||
</div>
|
||
<div class="card-body">
|
||
<p>Содержание параграфа <b>«Дробно-рациональные уравнения»</b> будет добавлено в следующих обновлениях.</p>
|
||
<p style="color:var(--muted);font-size:.9rem">Раздел Phase 1.</p>
|
||
</div>
|
||
</div>` + secNav(null, 'p11') + readButton('p10');
|
||
renderMath(root);
|
||
wireReadBtn('p10');
|
||
}
|
||
|
||
function buildP11(){
|
||
const root = document.getElementById('p11-body');
|
||
root.innerHTML = `
|
||
<div class="card">
|
||
<div class="card-header">
|
||
<span class="card-icon theory">${ICONS.theory}</span>
|
||
<span class="card-title">В разработке</span>
|
||
<span class="card-num">§ 11</span>
|
||
</div>
|
||
<div class="card-body">
|
||
<p>Содержание параграфа <b>«Системы нелинейных уравнений»</b> будет добавлено в следующих обновлениях.</p>
|
||
<p style="color:var(--muted);font-size:.9rem">Раздел Phase 1.</p>
|
||
</div>
|
||
</div>` + secNav('p10', 'p12') + readButton('p11');
|
||
renderMath(root);
|
||
wireReadBtn('p11');
|
||
}
|
||
|
||
function buildP12(){
|
||
const root = document.getElementById('p12-body');
|
||
root.innerHTML = `
|
||
<div class="card">
|
||
<div class="card-header">
|
||
<span class="card-icon theory">${ICONS.theory}</span>
|
||
<span class="card-title">В разработке</span>
|
||
<span class="card-num">§ 12</span>
|
||
</div>
|
||
<div class="card-body">
|
||
<p>Содержание параграфа <b>«Уравнение окружности»</b> будет добавлено в следующих обновлениях.</p>
|
||
<p style="color:var(--muted);font-size:.9rem">Раздел Phase 1.</p>
|
||
</div>
|
||
</div>` + secNav('p11', 'p13') + readButton('p12');
|
||
renderMath(root);
|
||
wireReadBtn('p12');
|
||
}
|
||
|
||
function buildP13(){
|
||
const root = document.getElementById('p13-body');
|
||
root.innerHTML = `
|
||
<div class="card">
|
||
<div class="card-header">
|
||
<span class="card-icon theory">${ICONS.theory}</span>
|
||
<span class="card-title">В разработке</span>
|
||
<span class="card-num">§ 13</span>
|
||
</div>
|
||
<div class="card-body">
|
||
<p>Содержание параграфа <b>«Метод интервалов»</b> будет добавлено в следующих обновлениях.</p>
|
||
<p style="color:var(--muted);font-size:.9rem">Раздел Phase 1.</p>
|
||
</div>
|
||
</div>` + secNav('p12', 'final3') + readButton('p13');
|
||
renderMath(root);
|
||
wireReadBtn('p13');
|
||
}
|
||
|
||
function buildFinal3(){
|
||
const root = document.getElementById('final3-body');
|
||
root.innerHTML = `
|
||
<div class="card">
|
||
<div class="card-header">
|
||
<span class="card-icon theory">${ICONS.theory}</span>
|
||
<span class="card-title">В разработке</span>
|
||
<span class="card-num">★</span>
|
||
</div>
|
||
<div class="card-body">
|
||
<p>Содержание финала главы <b>Финал главы — в разработке</b> будет добавлено в следующих обновлениях.</p>
|
||
<p style="color:var(--muted);font-size:.9rem">Боссы и итоговые задания будут добавлены в Phase 1.</p>
|
||
</div>
|
||
</div>` + secNav('p13', null) + readButton('final3');
|
||
renderMath(root);
|
||
wireReadBtn('final3');
|
||
}
|
||
|
||
/* ===== Search ===== */
|
||
const SEARCH_INDEX = (function(){
|
||
const arr=[];
|
||
PARAS.forEach(p=>arr.push({kind:'Параграф',title:p.num+' '+p.name,desc:p.sub||'',sec:p.id}));
|
||
return arr;
|
||
})();
|
||
function initSearch(){
|
||
const modal=document.getElementById('search-modal'),inp=document.getElementById('search-input'),out=document.getElementById('search-results'),btn=document.getElementById('search-btn');
|
||
if(!modal||!inp||!out) return;
|
||
let cur=0,rows=[];
|
||
function score(q,it){ const t=(it.title+' '+it.desc).toLowerCase(); if(t.includes(q)) return 100+(it.title.toLowerCase().startsWith(q)?50:0); let s=0; q.split(/\s+/).forEach(w=>{if(w&&t.includes(w))s+=10;}); return s; }
|
||
function rank(q){ q=q.trim().toLowerCase(); if(!q) return SEARCH_INDEX.slice(0,12); return SEARCH_INDEX.map(it=>({it,s:score(q,it)})).filter(x=>x.s>0).sort((a,b)=>b.s-a.s).slice(0,20).map(x=>x.it); }
|
||
function render(){ cur=0; if(!rows.length){out.innerHTML='<div class="search-empty">Ничего не найдено</div>';return;} out.innerHTML=rows.map((r,i)=>'<button class="search-row'+(i===0?' active':'')+'" data-i="'+i+'"><div class="sr-kind">'+r.kind+'</div><div class="sr-title">'+r.title+'</div>'+(r.desc?'<div class="sr-desc">'+(r.desc.length>90?r.desc.slice(0,90)+'…':r.desc)+'</div>':'')+'</button>').join(''); out.querySelectorAll('.search-row').forEach(b=>b.addEventListener('click',()=>{cur=+b.dataset.i;pick();})); }
|
||
function pick(){ const r=rows[cur]; if(!r) return; close(); goTo(r.sec); }
|
||
function move(d){ const items=out.querySelectorAll('.search-row'); if(!items.length) return; items[cur]&&items[cur].classList.remove('active'); cur=(cur+d+items.length)%items.length; items[cur].classList.add('active'); items[cur].scrollIntoView({block:'nearest'}); }
|
||
function open(){ modal.classList.add('show'); inp.value=''; rows=rank(''); render(); setTimeout(()=>inp.focus(),50); }
|
||
function close(){ modal.classList.remove('show'); }
|
||
btn&&btn.addEventListener('click',open);
|
||
modal.addEventListener('click',e=>{if(e.target===modal)close();});
|
||
inp.addEventListener('input',()=>{rows=rank(inp.value);render();});
|
||
inp.addEventListener('keydown',e=>{ if(e.key==='ArrowDown'){e.preventDefault();move(1);}else if(e.key==='ArrowUp'){e.preventDefault();move(-1);}else if(e.key==='Enter'){e.preventDefault();pick();}else if(e.key==='Escape'){e.preventDefault();close();} });
|
||
document.addEventListener('keydown',e=>{ if((e.ctrlKey||e.metaKey)&&(e.key==='k'||e.key==='K')){ e.preventDefault(); if(modal.classList.contains('show')) close(); else open(); } });
|
||
}
|
||
|
||
function initSidebarToggle(){
|
||
const side=document.getElementById('col-side'),back=document.getElementById('col-side-backdrop'),btn=document.getElementById('sidebar-btn');
|
||
if(!side||!btn) return;
|
||
function open(){ side.classList.add('open'); back.classList.add('show'); }
|
||
function close(){ side.classList.remove('open'); back.classList.remove('show'); }
|
||
btn.addEventListener('click',()=>{ if(side.classList.contains('open')) close(); else open(); });
|
||
back.addEventListener('click',close);
|
||
document.addEventListener('keydown',e=>{ if(e.key==='Escape') close(); });
|
||
}
|
||
|
||
function init(){
|
||
loadProgress(); initTheme(); initSidebarToggle(); initSearch();
|
||
buildParaSelector(); refreshProgressUI(); loadServerReadState(); goTo('p10');
|
||
setTimeout(()=>achievement('start'), 600);
|
||
if(window.LS&&window.LS.xp){
|
||
window.LS.xp.load().then(function(s){ if(s&&s.xp>STATE.xp){ STATE.xp=s.xp; STATE.level=calcLevel(STATE.xp); saveProgress(); refreshProgressUI(); if(STATE.current) buildSidebar(STATE.current); } });
|
||
}
|
||
}
|
||
document.addEventListener('DOMContentLoaded', init);
|
||
</script>
|
||
|
||
</body>
|
||
</html>
|