3x^2-48=0 eching

$$3 x ^ { 2 } - 48 = 0$$

x uchun yechish

$$x=4$$

$$x=-4$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 3 ga bo‘ling.

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

Hisoblang: x^{2}-16. x^{2}-16 ni x^{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).

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

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

$$x=4 x=-4$$

Kvadrat ildizini topish bo'yicha qadamlar

48 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$3x^{2}=48$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{48}{3}$$

16 ni olish uchun 48 ni 3 ga bo‘ling.

$$x^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=4 x=-4$$

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.

$$3x^{2}-48=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -48 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-48\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-48\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-48\right)}}{2\times 3}$$

-12 ni -48 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{576}}{2\times 3}$$

576 ning kvadrat ildizini chiqarish.

$$x=\frac{0±24}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±24}{6}$$

x=\frac{0±24}{6} tenglamasini yeching, bunda ± musbat. 24 ni 6 ga bo'lish.

$$x=4$$

x=\frac{0±24}{6} tenglamasini yeching, bunda ± manfiy. -24 ni 6 ga bo'lish.

$$x=-4$$

Tenglama yechildi.

$$x=4 x=-4$$