x^2+x^2-13=130 eching

$${ x }^{ 2 } + { x }^{ 2 } -13=130$$

x uchun yechish

$$x = \frac{\sqrt{286}}{2} \approx 8,455767263$$

$$x = -\frac{\sqrt{286}}{2} \approx -8,455767263$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$2x^{2}-13=130$$

13 ni ikki tarafga qo’shing.

$$2x^{2}=130+13$$

143 olish uchun 130 va 13'ni qo'shing.

$$2x^{2}=143$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{143}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{286}}{2} x=-\frac{\sqrt{286}}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$2x^{2}-13=130$$

Ikkala tarafdan 130 ni ayirish.

$$2x^{2}-13-130=0$$

-143 olish uchun -13 dan 130 ni ayirish.

$$2x^{2}-143=0$$

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 -143 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-143\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-143\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-143\right)}}{2\times 2}$$

-8 ni -143 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1144}}{2\times 2}$$

1144 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{286}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{286}}{4}$$

x=\frac{0±2\sqrt{286}}{4} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{286}}{2}$$

x=\frac{0±2\sqrt{286}}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{286}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{286}}{2} x=-\frac{\sqrt{286}}{2}$$