2x^2-3=0 eching

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

x uchun yechish

$$x = \frac{\sqrt{6}}{2} \approx 1,224744871$$

$$x = -\frac{\sqrt{6}}{2} \approx -1,224744871$$

Kvadrat ildizini topish bo'yicha qadamlar

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

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

Ikki tarafini 2 ga bo‘ling.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{6}}{2} x=-\frac{\sqrt{6}}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

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

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 -3 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-3\right)}}{2\times 2}$$

-8 ni -3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{24}}{2\times 2}$$

24 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{6}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{6}}{4}$$

x=\frac{0±2\sqrt{6}}{4} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±2\sqrt{6}}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{6}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{6}}{2} x=-\frac{\sqrt{6}}{2}$$