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Pozdravljeni v videu o [br]dopolnjevanju kvadratov.

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Kaj je dopolnjevanje kvadratov?

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Je eden od načinov [br]reševanja kvadratnih enačb.

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Preden -- no, naj napišem[br]kvadratno enačbo

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nato pa bom pokazal,[br]kako dopolniti kvadrat.

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Pozneje bom naredili še en primer,[br]mogoče še enega, potem pa

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bomo povedali, zakaj to imenujemo[br]dopolnjevanje kvadratov.

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Imamo npr. naslednjo enačbo:[br]x na kvadrat plus 16x

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minus 57 je enako 0.

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Torej... ali že znamo kaj,[br]kar bi nam lahko pomagalo

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rešiti ta problem?

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Lahko poskusimo s faktorizacijo.

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Kateri dve števili seštejemo, [br]da dobimo 16, in zmnožimo,

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da dobimo -57?

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Verjetno morate malo premisliti.

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Lahko bomo dobili cela[br]števila, vendar nismo niti

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prepričani, da obstajata[br]celi števili, ki data

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tak rezultat.

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V tem primeru obstajata.

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Ampak včasih je rešitev[br]decimalno število,

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pa tega ne vemo.

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Torej, faktorizacija je uporabna[br]samo, če smo prepričani,

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da lahko najdemo primerna[br]cela števila.

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Se pravi, x plus celo število[br]ali x minus celo število

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krat x plus neko celo število.

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Ali nekaj podobnega.

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Druga možnost je reševanje[br]kvadratne enačbe.

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Videli bomo, da [br]je kvadratna enačba

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samo bližnjica do dopolnitve kvadratov.

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Kvadratno enačbo [br]celo dokažemo z dopolnitvijo

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kvadrata.

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Kaj je torej dopolnitev kvadrata?

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Kaj naredimo?

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