2x^2-1=4 eching

$$2 x ^ { 2 } - 1 = 4$$

x uchun yechish

$$x = \frac{\sqrt{10}}{2} \approx 1,58113883$$

$$x = -\frac{\sqrt{10}}{2} \approx -1,58113883$$

Kvadrat ildizini topish bo'yicha qadamlar

1 ni ikki tarafga qo’shing.

$$2x^{2}=4+1$$

5 olish uchun 4 va 1'ni qo'shing.

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

Ikki tarafini 2 ga bo‘ling.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 4 ni ayirish.

$$2x^{2}-1-4=0$$

-5 olish uchun -1 dan 4 ni ayirish.

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

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 -5 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-5\right)}}{2\times 2}$$

-8 ni -5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{40}}{2\times 2}$$

40 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{10}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{10}}{4}$$

x=\frac{0±2\sqrt{10}}{4} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{10}}{2}$$

x=\frac{0±2\sqrt{10}}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{10}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$