9x^2=16 eching

$$9 { x }^{ 2 } =16$$

x uchun yechish

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1,333333333$$

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1,333333333$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 9 ga bo‘ling.

$$x^{2}=\frac{16}{9}$$

Ikkala tarafdan \frac{16}{9} ni ayirish.

$$x^{2}-\frac{16}{9}=0$$

Ikkala tarafini 9 ga ko‘paytiring.

$$9x^{2}-16=0$$

Hisoblang: 9x^{2}-16. 9x^{2}-16 ni \left(3x\right)^{2}-4^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-4\right)\left(3x+4\right)=0$$

Tenglamani yechish uchun 3x-4=0 va 3x+4=0 ni yeching.

$$x=\frac{4}{3} x=-\frac{4}{3}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 9 ga bo‘ling.

$$x^{2}=\frac{16}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{4}{3} x=-\frac{4}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 9 ga bo‘ling.

$$x^{2}=\frac{16}{9}$$

Ikkala tarafdan \frac{16}{9} ni ayirish.

$$x^{2}-\frac{16}{9}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -\frac{16}{9} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{16}{9}\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{16}{9}\right)}}{2}$$

-4 ni -\frac{16}{9} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{64}{9}}}{2}$$

\frac{64}{9} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{8}{3}}{2}$$

x=\frac{0±\frac{8}{3}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\frac{4}{3}$$

x=\frac{0±\frac{8}{3}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{4}{3}$$

Tenglama yechildi.

$$x=\frac{4}{3} x=-\frac{4}{3}$$