(z+1)(z-1)=1 eching

$$( z + 1 ) ( z - 1 ) = 1$$

z uchun yechish

$$z=\sqrt{2}\approx 1,414213562$$

$$z=-\sqrt{2}\approx -1,414213562$$

Kvadrat ildizini topish bo'yicha qadamlar

Hisoblang: \left(z+1\right)\left(z-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.

$$z^{2}-1=1$$

1 ni ikki tarafga qo’shing.

$$z^{2}=1+1$$

2 olish uchun 1 va 1'ni qo'shing.

$$z^{2}=2$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$z=\sqrt{2} z=-\sqrt{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(z+1\right)\left(z-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.

$$z^{2}-1=1$$

Ikkala tarafdan 1 ni ayirish.

$$z^{2}-1-1=0$$

-2 olish uchun -1 dan 1 ni ayirish.

$$z^{2}-2=0$$

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 -2 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -2 marotabaga ko'paytirish.

$$z=\frac{0±\sqrt{8}}{2}$$

8 ning kvadrat ildizini chiqarish.

$$z=\frac{0±2\sqrt{2}}{2}$$

z=\frac{0±2\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat.

$$z=\sqrt{2}$$

z=\frac{0±2\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy.

$$z=-\sqrt{2}$$

Tenglama yechildi.

$$z=\sqrt{2} z=-\sqrt{2}$$