5x^2-2=1 eching

$$5 x ^ { 2 } - 2 = 1$$

x uchun yechish

$$x=\frac{\sqrt{15}}{5}\approx 0,774596669$$

$$x=-\frac{\sqrt{15}}{5}\approx -0,774596669$$

Kvadrat ildizini topish bo'yicha qadamlar

2 ni ikki tarafga qo’shing.

$$5x^{2}=1+2$$

3 olish uchun 1 va 2'ni qo'shing.

$$5x^{2}=3$$

Ikki tarafini 5 ga bo‘ling.

$$x^{2}=\frac{3}{5}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{15}}{5} x=-\frac{\sqrt{15}}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1 ni ayirish.

$$5x^{2}-2-1=0$$

-3 olish uchun -2 dan 1 ni ayirish.

$$5x^{2}-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 0 ni b va -3 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-3\right)}}{2\times 5}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 5\left(-3\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-20\left(-3\right)}}{2\times 5}$$

-20 ni -3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{60}}{2\times 5}$$

60 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{15}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{15}}{10}$$

x=\frac{0±2\sqrt{15}}{10} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{15}}{5}$$

x=\frac{0±2\sqrt{15}}{10} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{15}}{5}$$

Tenglama yechildi.

$$x=\frac{\sqrt{15}}{5} x=-\frac{\sqrt{15}}{5}$$