{"version":"1.0","provider_name":"Studijni-svet.cz","provider_url":"https:\/\/studijni-svet.cz\/kurzy","author_name":"Studijni-svet.cz","author_url":"https:\/\/studijni-svet.cz\/kurzy\/author\/admin\/","title":"\u0158e\u0161en\u00fd p\u0159\u00edklad 2 | Studijni-svet.cz","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"COvWIVs9dI\"><a href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseny-priklad-2-3\/\">\u0158e\u0161en\u00fd p\u0159\u00edklad 2<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseny-priklad-2-3\/embed\/#?secret=COvWIVs9dI\" width=\"600\" height=\"338\" title=\"&#8222;\u0158e\u0161en\u00fd p\u0159\u00edklad 2&#8220; &#8212; Studijni-svet.cz\" data-secret=\"COvWIVs9dI\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script>\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/\/# sourceURL=https:\/\/studijni-svet.cz\/kurzy\/wp-includes\/js\/wp-embed.min.js\n<\/script>\n","description":"Zad\u00e1n\u00ed: \u0158e\u0161t\u011b v oboru R rovnici: $$sqrt{x+1}+sqrt{x+2}=sqrt{4x+5}$$ &nbsp; \u0158e\u0161en\u00ed: Celou rovnice umocn\u00edme: $$sqrt{x+1}+sqrt{x+2}=sqrt{4x+5}\/\u00b2$$ $${(sqrt{x+1}+sqrt{x+2})}^{2}={(sqrt{4x+5})}^{2}$$ M\u00e1me na pam\u011bti to, \u017ee v\u00fdraz na lev\u00e9 stran\u011b rovnice mus\u00edme umocnit podle vzorce: (a+b)\u00b2=a\u00b2+2ab+b\u00b2, kde\u00a0a=\u221ax+1\u00a0a\u00a0b=\u221ax+2 $$x+1+2sqrt{x+1}sqrt{x+2}+x+2=4x+5$$ $$2x+3+2sqrt{x+1}sqrt{x+2}=4x+5$$ $$-2+2sqrt{x+1}sqrt{x+2}=2x\/:2$$ $$-1+sqrt{x+1}sqrt{x+2}=x\/\u00b2$$ $${(-1)}^{2}+(x+1)(x+2)=x^{2}$$ $$1+{x}^{2}+2x+x+2=x^{2}$$ $$3x=-3$$ $$x=-1$$ Ne\u017e prohl\u00e1s\u00edme v\u00fdsledek za spr\u00e1vn\u00fd, mus\u00edme prov\u00e9st zkou\u0161ku $$L(-1)=sqrt{(-1)+1}+sqrt{(-1)+2}=sqrt{0}+sqrt{1}=1$$ $$P(-1)=sqrt{4(-1)+5}=sqrt{1}=1$$ $$L=P$$ K={-1}"}