-4/3x^2+12=0 eching

$$- \frac { 4 } { 3 } x ^ { 2 } + 12 = 0$$

x uchun yechish

$$x=3$$

$$x=-3$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 12 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-\frac{4}{3}x^{2}=-12$$

Ikki tarafini -\frac{3}{4} va teskari kasri -\frac{4}{3} ga ko‘paytiring.

$$x^{2}=-12\left(-\frac{3}{4}\right)$$

9 hosil qilish uchun -12 va -\frac{3}{4} ni ko'paytirish.

$$x^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=3 x=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$-\frac{4}{3}x^{2}+12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -\frac{4}{3} ni a, 0 ni b va 12 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{4}{3}\right)\times 12}}{2\left(-\frac{4}{3}\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{4}{3}\right)\times 12}}{2\left(-\frac{4}{3}\right)}$$

-4 ni -\frac{4}{3} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{16}{3}\times 12}}{2\left(-\frac{4}{3}\right)}$$

\frac{16}{3} ni 12 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{64}}{2\left(-\frac{4}{3}\right)}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8}{2\left(-\frac{4}{3}\right)}$$

2 ni -\frac{4}{3} marotabaga ko'paytirish.

$$x=\frac{0±8}{-\frac{8}{3}}$$

x=\frac{0±8}{-\frac{8}{3}} tenglamasini yeching, bunda ± musbat. 8 ni -\frac{8}{3} ga bo'lish 8 ga k'paytirish -\frac{8}{3} ga qaytarish.

$$x=-3$$

x=\frac{0±8}{-\frac{8}{3}} tenglamasini yeching, bunda ± manfiy. -8 ni -\frac{8}{3} ga bo'lish -8 ga k'paytirish -\frac{8}{3} ga qaytarish.

$$x=3$$

Tenglama yechildi.

$$x=-3 x=3$$