(x+3)(x-3)=5 eching

$$( x + 3 ) ( x - 3 ) = 5$$

x uchun yechish

$$x=\sqrt{14}\approx 3,741657387$$

$$x=-\sqrt{14}\approx -3,741657387$$

Kvadrat ildizini topish bo'yicha qadamlar

Hisoblang: \left(x+3\right)\left(x-3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$x^{2}-9=5$$

9 ni ikki tarafga qo’shing.

$$x^{2}=5+9$$

14 olish uchun 5 va 9'ni qo'shing.

$$x^{2}=14$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{14} x=-\sqrt{14}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(x+3\right)\left(x-3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$x^{2}-9=5$$

Ikkala tarafdan 5 ni ayirish.

$$x^{2}-9-5=0$$

-14 olish uchun -9 dan 5 ni ayirish.

$$x^{2}-14=0$$

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 -14 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-14\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-14\right)}}{2}$$

-4 ni -14 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{56}}{2}$$

56 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{14}}{2}$$

x=\frac{0±2\sqrt{14}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{14}$$

x=\frac{0±2\sqrt{14}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{14}$$

Tenglama yechildi.

$$x=\sqrt{14} x=-\sqrt{14}$$