3z^2=1024 eching

$$3 z ^ { 2 } = 1024$$

z uchun yechish

$$z = \frac{32 \sqrt{3}}{3} \approx 18,475208614$$

$$z = -\frac{32 \sqrt{3}}{3} \approx -18,475208614$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 3 ga bo‘ling.

$$z^{2}=\frac{1024}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$z=\frac{32\sqrt{3}}{3} z=-\frac{32\sqrt{3}}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 3 ga bo‘ling.

$$z^{2}=\frac{1024}{3}$$

Ikkala tarafdan \frac{1024}{3} ni ayirish.

$$z^{2}-\frac{1024}{3}=0$$

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{1024}{3} ni c bilan almashtiring.

$$z=\frac{0±\sqrt{0^{2}-4\left(-\frac{1024}{3}\right)}}{2}$$

0 kvadratini chiqarish.

$$z=\frac{0±\sqrt{-4\left(-\frac{1024}{3}\right)}}{2}$$

-4 ni -\frac{1024}{3} marotabaga ko'paytirish.

$$z=\frac{0±\sqrt{\frac{4096}{3}}}{2}$$

\frac{4096}{3} ning kvadrat ildizini chiqarish.

$$z=\frac{0±\frac{64\sqrt{3}}{3}}{2}$$

z=\frac{0±\frac{64\sqrt{3}}{3}}{2} tenglamasini yeching, bunda ± musbat.

$$z=\frac{32\sqrt{3}}{3}$$

z=\frac{0±\frac{64\sqrt{3}}{3}}{2} tenglamasini yeching, bunda ± manfiy.

$$z=-\frac{32\sqrt{3}}{3}$$

Tenglama yechildi.

$$z=\frac{32\sqrt{3}}{3} z=-\frac{32\sqrt{3}}{3}$$