4x^2-6=2x^2 eching

$$4 x ^ { 2 } - 6 = 2 x ^ { 2 }$$

x uchun yechish

$$x=\sqrt{3}\approx 1,732050808$$

$$x=-\sqrt{3}\approx -1,732050808$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 2x^{2} ni ayirish.

$$4x^{2}-6-2x^{2}=0$$

2x^{2} ni olish uchun 4x^{2} va -2x^{2} ni birlashtirish.

$$2x^{2}-6=0$$

6 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2x^{2}=6$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{6}{2}$$

3 ni olish uchun 6 ni 2 ga bo‘ling.

$$x^{2}=3$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{3} x=-\sqrt{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x^{2} ni ayirish.

$$4x^{2}-6-2x^{2}=0$$

2x^{2} ni olish uchun 4x^{2} va -2x^{2} ni birlashtirish.

$$2x^{2}-6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 0 ni b va -6 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-6\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-6\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-6\right)}}{2\times 2}$$

-8 ni -6 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{48}}{2\times 2}$$

48 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{3}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{3}}{4}$$

x=\frac{0±4\sqrt{3}}{4} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{3}$$

x=\frac{0±4\sqrt{3}}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{3}$$

Tenglama yechildi.

$$x=\sqrt{3} x=-\sqrt{3}$$