3x^2-1=0 eching

$$3 x ^ { 2 } - 1 = 0$$

x uchun yechish

$$x=\frac{\sqrt{3}}{3}\approx 0,577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0,577350269$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$3x^{2}=1$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{1}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

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.

$$3x^{2}-1=0$$

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 -1 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-1\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-1\right)}}{2\times 3}$$

-12 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{12}}{2\times 3}$$

12 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{3}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{3}}{6}$$

x=\frac{0±2\sqrt{3}}{6} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±2\sqrt{3}}{6} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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