(2008-x)(2006-x)=2007 eching

$$(2008-x)(2006-x)=2007$$

x uchun yechish

$$x=2007-2\sqrt{502}\approx 1962,189286995$$

$$x=2\sqrt{502}+2007\approx 2051,810713005$$

Kvadrat tenglamalaridan foydalanish qoidalari

2008-x ga 2006-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4028048-4014x+x^{2}=2007$$

Ikkala tarafdan 2007 ni ayirish.

$$4028048-4014x+x^{2}-2007=0$$

4026041 olish uchun 4028048 dan 2007 ni ayirish.

$$4026041-4014x+x^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x^{2}-4014x+4026041=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -4014 ni b va 4026041 ni c bilan almashtiring.

$$x=\frac{-\left(-4014\right)±\sqrt{\left(-4014\right)^{2}-4\times 4026041}}{2}$$

-4014 kvadratini chiqarish.

$$x=\frac{-\left(-4014\right)±\sqrt{16112196-4\times 4026041}}{2}$$

-4 ni 4026041 marotabaga ko'paytirish.

$$x=\frac{-\left(-4014\right)±\sqrt{16112196-16104164}}{2}$$

16112196 ni -16104164 ga qo'shish.

$$x=\frac{-\left(-4014\right)±\sqrt{8032}}{2}$$

8032 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4014\right)±4\sqrt{502}}{2}$$

-4014 ning teskarisi 4014 ga teng.

$$x=\frac{4014±4\sqrt{502}}{2}$$

x=\frac{4014±4\sqrt{502}}{2} tenglamasini yeching, bunda ± musbat. 4014 ni 4\sqrt{502} ga qo'shish.

$$x=\frac{4\sqrt{502}+4014}{2}$$

4014+4\sqrt{502} ni 2 ga bo'lish.

$$x=2\sqrt{502}+2007$$

x=\frac{4014±4\sqrt{502}}{2} tenglamasini yeching, bunda ± manfiy. 4014 dan 4\sqrt{502} ni ayirish.

$$x=\frac{4014-4\sqrt{502}}{2}$$

4014-4\sqrt{502} ni 2 ga bo'lish.

$$x=2007-2\sqrt{502}$$

Tenglama yechildi.

$$x=2\sqrt{502}+2007 x=2007-2\sqrt{502}$$

Kvadratni yakunlash bo'yicha qadamlar

2008-x ga 2006-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4028048-4014x+x^{2}=2007$$

Ikkala tarafdan 4028048 ni ayirish.

$$-4014x+x^{2}=2007-4028048$$

-4026041 olish uchun 2007 dan 4028048 ni ayirish.

$$-4014x+x^{2}=-4026041$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}-4014x=-4026041$$

-4014 ni bo‘lish, x shartining koeffitsienti, 2 ga -2007 olish uchun. Keyin, -2007 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-4014x+\left(-2007\right)^{2}=-4026041+\left(-2007\right)^{2}$$

-2007 kvadratini chiqarish.

$$x^{2}-4014x+4028049=-4026041+4028049$$

-4026041 ni 4028049 ga qo'shish.

$$x^{2}-4014x+4028049=2008$$

x^{2}-4014x+4028049 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-2007\right)^{2}=2008$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2007\right)^{2}}=\sqrt{2008}$$

Qisqartirish.

$$x-2007=2\sqrt{502} x-2007=-2\sqrt{502}$$

2007 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{502}+2007 x=2007-2\sqrt{502}$$