3x^2-7=11 eching

$$3 x ^ { 2 } - 7 = 11$$

x uchun yechish

$$x=\sqrt{6}\approx 2,449489743$$

$$x=-\sqrt{6}\approx -2,449489743$$

Kvadrat ildizini topish bo'yicha qadamlar

7 ni ikki tarafga qo’shing.

$$3x^{2}=11+7$$

18 olish uchun 11 va 7'ni qo'shing.

$$3x^{2}=18$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{18}{3}$$

6 ni olish uchun 18 ni 3 ga bo‘ling.

$$x^{2}=6$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{6} x=-\sqrt{6}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 11 ni ayirish.

$$3x^{2}-7-11=0$$

-18 olish uchun -7 dan 11 ni ayirish.

$$3x^{2}-18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -18 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-18\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-18\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-18\right)}}{2\times 3}$$

-12 ni -18 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{216}}{2\times 3}$$

216 ning kvadrat ildizini chiqarish.

$$x=\frac{0±6\sqrt{6}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±6\sqrt{6}}{6}$$

x=\frac{0±6\sqrt{6}}{6} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{6}$$

x=\frac{0±6\sqrt{6}}{6} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{6}$$

Tenglama yechildi.

$$x=\sqrt{6} x=-\sqrt{6}$$