1/3x^2-3=0 eching

$$\frac { 1 } { 3 } x ^ { 2 } - 3 = 0$$

x uchun yechish

$$x=3$$

$$x=-3$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafini 3 ga ko‘paytiring.

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

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

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

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

$$x=3 x=-3$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$\frac{1}{3}x^{2}=3$$

Ikki tarafini 3 va teskari kasri \frac{1}{3} ga ko‘paytiring.

$$x^{2}=3\times 3$$

9 hosil qilish uchun 3 va 3 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.

$$\frac{1}{3}x^{2}-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{3} ni a, 0 ni b va -3 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{3}\left(-3\right)}}{2\times \frac{1}{3}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{1}{3}\left(-3\right)}}{2\times \frac{1}{3}}$$

-4 ni \frac{1}{3} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-\frac{4}{3}\left(-3\right)}}{2\times \frac{1}{3}}$$

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

$$x=\frac{0±\sqrt{4}}{2\times \frac{1}{3}}$$

4 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2}{2\times \frac{1}{3}}$$

2 ni \frac{1}{3} marotabaga ko'paytirish.

$$x=\frac{0±2}{\frac{2}{3}}$$

x=\frac{0±2}{\frac{2}{3}} tenglamasini yeching, bunda ± musbat. 2 ni \frac{2}{3} ga bo'lish 2 ga k'paytirish \frac{2}{3} ga qaytarish.

$$x=3$$

x=\frac{0±2}{\frac{2}{3}} tenglamasini yeching, bunda ± manfiy. -2 ni \frac{2}{3} ga bo'lish -2 ga k'paytirish \frac{2}{3} ga qaytarish.

$$x=-3$$

Tenglama yechildi.

$$x=3 x=-3$$