(x-1)(x+1)=15 eching

$$(x-1)(x+1)=15$$

x uchun yechish

$$x=-4$$

$$x=4$$

Kvadrat ildizini topish bo'yicha qadamlar

Hisoblang: \left(x-1\right)\left(x+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$x^{2}-1=15$$

1 ni ikki tarafga qo’shing.

$$x^{2}=15+1$$

16 olish uchun 15 va 1'ni qo'shing.

$$x^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=4 x=-4$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(x-1\right)\left(x+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$x^{2}-1=15$$

Ikkala tarafdan 15 ni ayirish.

$$x^{2}-1-15=0$$

-16 olish uchun -1 dan 15 ni ayirish.

$$x^{2}-16=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -16 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

-4 ni -16 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{64}}{2}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8}{2}$$

x=\frac{0±8}{2} tenglamasini yeching, bunda ± musbat. 8 ni 2 ga bo'lish.

$$x=4$$

x=\frac{0±8}{2} tenglamasini yeching, bunda ± manfiy. -8 ni 2 ga bo'lish.

$$x=-4$$

Tenglama yechildi.

$$x=4 x=-4$$