96-2z^2-4z^2=0 eching

$$96 - 2 z ^ { 2 } - 4 z ^ { 2 } = 0$$

z uchun yechish

$$z=4$$

$$z=-4$$

Kvadrat ildizini topish bo'yicha qadamlar

-6z^{2} ni olish uchun -2z^{2} va -4z^{2} ni birlashtirish.

$$96-6z^{2}=0$$

Ikkala tarafdan 96 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-6z^{2}=-96$$

Ikki tarafini -6 ga bo‘ling.

$$z^{2}=\frac{-96}{-6}$$

16 ni olish uchun -96 ni -6 ga bo‘ling.

$$z^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$z=4 z=-4$$

Kvadrat tenglamalaridan foydalanish qoidalari

-6z^{2} ni olish uchun -2z^{2} va -4z^{2} ni birlashtirish.

$$96-6z^{2}=0$$

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.

$$-6z^{2}+96=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -6 ni a, 0 ni b va 96 ni c bilan almashtiring.

$$z=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 96}}{2\left(-6\right)}$$

0 kvadratini chiqarish.

$$z=\frac{0±\sqrt{-4\left(-6\right)\times 96}}{2\left(-6\right)}$$

-4 ni -6 marotabaga ko'paytirish.

$$z=\frac{0±\sqrt{24\times 96}}{2\left(-6\right)}$$

24 ni 96 marotabaga ko'paytirish.

$$z=\frac{0±\sqrt{2304}}{2\left(-6\right)}$$

2304 ning kvadrat ildizini chiqarish.

$$z=\frac{0±48}{2\left(-6\right)}$$

2 ni -6 marotabaga ko'paytirish.

$$z=\frac{0±48}{-12}$$

z=\frac{0±48}{-12} tenglamasini yeching, bunda ± musbat. 48 ni -12 ga bo'lish.

$$z=-4$$

z=\frac{0±48}{-12} tenglamasini yeching, bunda ± manfiy. -48 ni -12 ga bo'lish.

$$z=4$$

Tenglama yechildi.

$$z=-4 z=4$$