0=1/3*x^2-9 eching

$$0 = \frac { 1 } { 3 } \cdot x ^ { 2 } - 9$$

x uchun yechish

$$x=3\sqrt{3}\approx 5,196152423$$

$$x=-3\sqrt{3}\approx -5,196152423$$

Kvadrat ildizini topish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1}{3}x^{2}-9=0$$

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

$$\frac{1}{3}x^{2}=9$$

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

$$x^{2}=9\times 3$$

27 hosil qilish uchun 9 va 3 ni ko'paytirish.

$$x^{2}=27$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=3\sqrt{3} x=-3\sqrt{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1}{3}x^{2}-9=0$$

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 -9 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{3}\left(-9\right)}}{2\times \frac{1}{3}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{1}{3}\left(-9\right)}}{2\times \frac{1}{3}}$$

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

$$x=\frac{0±\sqrt{-\frac{4}{3}\left(-9\right)}}{2\times \frac{1}{3}}$$

-\frac{4}{3} ni -9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{12}}{2\times \frac{1}{3}}$$

12 ning kvadrat ildizini chiqarish.

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

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

$$x=\frac{0±2\sqrt{3}}{\frac{2}{3}}$$

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

$$x=3\sqrt{3}$$

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

$$x=-3\sqrt{3}$$

Tenglama yechildi.

$$x=3\sqrt{3} x=-3\sqrt{3}$$