3x*1/4x=108 eching

$$3 x \cdot \frac { 1 } { 4 } x = 108$$

x uchun yechish

$$x=12$$

$$x=-12$$

Kvadrat ildizini topish bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$3x^{2}\times \frac{1}{4}=108$$

\frac{3}{4} hosil qilish uchun 3 va \frac{1}{4} ni ko'paytirish.

$$\frac{3}{4}x^{2}=108$$

Ikki tarafini \frac{4}{3} va teskari kasri \frac{3}{4} ga ko‘paytiring.

$$x^{2}=108\times \frac{4}{3}$$

108\times \frac{4}{3} ni yagona kasrga aylantiring.

$$x^{2}=\frac{108\times 4}{3}$$

432 hosil qilish uchun 108 va 4 ni ko'paytirish.

$$x^{2}=\frac{432}{3}$$

144 ni olish uchun 432 ni 3 ga bo‘ling.

$$x^{2}=144$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=12 x=-12$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$3x^{2}\times \frac{1}{4}=108$$

\frac{3}{4} hosil qilish uchun 3 va \frac{1}{4} ni ko'paytirish.

$$\frac{3}{4}x^{2}=108$$

Ikkala tarafdan 108 ni ayirish.

$$\frac{3}{4}x^{2}-108=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{3}{4} ni a, 0 ni b va -108 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{4}\left(-108\right)}}{2\times \frac{3}{4}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{3}{4}\left(-108\right)}}{2\times \frac{3}{4}}$$

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

$$x=\frac{0±\sqrt{-3\left(-108\right)}}{2\times \frac{3}{4}}$$

-3 ni -108 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{324}}{2\times \frac{3}{4}}$$

324 ning kvadrat ildizini chiqarish.

$$x=\frac{0±18}{2\times \frac{3}{4}}$$

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

$$x=\frac{0±18}{\frac{3}{2}}$$

x=\frac{0±18}{\frac{3}{2}} tenglamasini yeching, bunda ± musbat. 18 ni \frac{3}{2} ga bo'lish 18 ga k'paytirish \frac{3}{2} ga qaytarish.

$$x=12$$

x=\frac{0±18}{\frac{3}{2}} tenglamasini yeching, bunda ± manfiy. -18 ni \frac{3}{2} ga bo'lish -18 ga k'paytirish \frac{3}{2} ga qaytarish.

$$x=-12$$

Tenglama yechildi.

$$x=12 x=-12$$