x^2+2x^2=24 eching

$$x ^ { 2 } + 2 x ^ { 2 } = 24$$

x uchun yechish

$$x=2\sqrt{2}\approx 2,828427125$$

$$x=-2\sqrt{2}\approx -2,828427125$$

Kvadrat ildizini topish bo'yicha qadamlar

3x^{2} ni olish uchun x^{2} va 2x^{2} ni birlashtirish.

$$3x^{2}=24$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{24}{3}$$

8 ni olish uchun 24 ni 3 ga bo‘ling.

$$x^{2}=8$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

3x^{2} ni olish uchun x^{2} va 2x^{2} ni birlashtirish.

$$3x^{2}=24$$

Ikkala tarafdan 24 ni ayirish.

$$3x^{2}-24=0$$

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 -24 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-24\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-24\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-24\right)}}{2\times 3}$$

-12 ni -24 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{288}}{2\times 3}$$

288 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12\sqrt{2}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±12\sqrt{2}}{6}$$

x=\frac{0±12\sqrt{2}}{6} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±12\sqrt{2}}{6} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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