(x-2)(x+2)=16 eching

$$(x-2)(x+2)=16$$

x uchun yechish

$$x=2\sqrt{5}\approx 4,472135955$$

$$x=-2\sqrt{5}\approx -4,472135955$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$x^{2}-4=16$$

4 ni ikki tarafga qo’shing.

$$x^{2}=16+4$$

20 olish uchun 16 va 4'ni qo'shing.

$$x^{2}=20$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2\sqrt{5} x=-2\sqrt{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}-4=16$$

Ikkala tarafdan 16 ni ayirish.

$$x^{2}-4-16=0$$

-20 olish uchun -4 dan 16 ni ayirish.

$$x^{2}-20=0$$

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 -20 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-20\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-20\right)}}{2}$$

-4 ni -20 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{80}}{2}$$

80 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{5}}{2}$$

x=\frac{0±4\sqrt{5}}{2} tenglamasini yeching, bunda ± musbat.

$$x=2\sqrt{5}$$

x=\frac{0±4\sqrt{5}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-2\sqrt{5}$$

Tenglama yechildi.

$$x=2\sqrt{5} x=-2\sqrt{5}$$