2^2+9x^2=12 eching

$$2 ^ { 2 } + 9 x ^ { 2 } = 12$$

x uchun yechish

$$x=\frac{2\sqrt{2}}{3}\approx 0,942809042$$

$$x=-\frac{2\sqrt{2}}{3}\approx -0,942809042$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$4+9x^{2}=12$$

Ikkala tarafdan 4 ni ayirish.

$$9x^{2}=12-4$$

8 olish uchun 12 dan 4 ni ayirish.

$$9x^{2}=8$$

Ikki tarafini 9 ga bo‘ling.

$$x^{2}=\frac{8}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{2\sqrt{2}}{3} x=-\frac{2\sqrt{2}}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$4+9x^{2}=12$$

Ikkala tarafdan 12 ni ayirish.

$$4+9x^{2}-12=0$$

-8 olish uchun 4 dan 12 ni ayirish.

$$-8+9x^{2}=0$$

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.

$$9x^{2}-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 9 ni a, 0 ni b va -8 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-8\right)}}{2\times 9}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 9\left(-8\right)}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-36\left(-8\right)}}{2\times 9}$$

-36 ni -8 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{288}}{2\times 9}$$

288 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12\sqrt{2}}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{0±12\sqrt{2}}{18}$$

x=\frac{0±12\sqrt{2}}{18} tenglamasini yeching, bunda ± musbat.

$$x=\frac{2\sqrt{2}}{3}$$

x=\frac{0±12\sqrt{2}}{18} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{2\sqrt{2}}{3}$$

Tenglama yechildi.

$$x=\frac{2\sqrt{2}}{3} x=-\frac{2\sqrt{2}}{3}$$