1/3(6x^2-4)=11 eching

$$1 / 3 ( 6 x ^ { 2 } - 4 ) = 11$$

x uchun yechish

$$x = \frac{\sqrt{222}}{6} \approx 2,483277404$$

$$x = -\frac{\sqrt{222}}{6} \approx -2,483277404$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$6x^{2}-4=11\times 3$$

33 hosil qilish uchun 11 va 3 ni ko'paytirish.

$$6x^{2}-4=33$$

4 ni ikki tarafga qo’shing.

$$6x^{2}=33+4$$

37 olish uchun 33 va 4'ni qo'shing.

$$6x^{2}=37$$

Ikki tarafini 6 ga bo‘ling.

$$x^{2}=\frac{37}{6}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{222}}{6} x=-\frac{\sqrt{222}}{6}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$6x^{2}-4=11\times 3$$

33 hosil qilish uchun 11 va 3 ni ko'paytirish.

$$6x^{2}-4=33$$

Ikkala tarafdan 33 ni ayirish.

$$6x^{2}-4-33=0$$

-37 olish uchun -4 dan 33 ni ayirish.

$$6x^{2}-37=0$$

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 -37 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-37\right)}}{2\times 6}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 6\left(-37\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-24\left(-37\right)}}{2\times 6}$$

-24 ni -37 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{888}}{2\times 6}$$

888 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{222}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{222}}{12}$$

x=\frac{0±2\sqrt{222}}{12} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{222}}{6}$$

x=\frac{0±2\sqrt{222}}{12} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{222}}{6}$$

Tenglama yechildi.

$$x=\frac{\sqrt{222}}{6} x=-\frac{\sqrt{222}}{6}$$