1/3x^2=49/3 eching

$$\frac{ 1 }{ 3 } { x }^{ 2 } = \frac{ 49 }{ 3 }$$

x uchun yechish

$$x=7$$

$$x=-7$$

Kvadratlar farqidan foydalangan qadamlar

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

$$x^{2}=\frac{49}{3}\times 3$$

49 hosil qilish uchun \frac{49}{3} va 3 ni ko'paytirish.

$$x^{2}=49$$

Ikkala tarafdan 49 ni ayirish.

$$x^{2}-49=0$$

Hisoblang: x^{2}-49. x^{2}-49 ni x^{2}-7^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-7\right)\left(x+7\right)=0$$

Tenglamani yechish uchun x-7=0 va x+7=0 ni yeching.

$$x=7 x=-7$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$x^{2}=\frac{49}{3}\times 3$$

49 hosil qilish uchun \frac{49}{3} va 3 ni ko'paytirish.

$$x^{2}=49$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=7 x=-7$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}=\frac{49}{3}\times 3$$

49 hosil qilish uchun \frac{49}{3} va 3 ni ko'paytirish.

$$x^{2}=49$$

Ikkala tarafdan 49 ni ayirish.

$$x^{2}-49=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -49 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-49\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-49\right)}}{2}$$

-4 ni -49 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{196}}{2}$$

196 ning kvadrat ildizini chiqarish.

$$x=\frac{0±14}{2}$$

x=\frac{0±14}{2} tenglamasini yeching, bunda ± musbat. 14 ni 2 ga bo'lish.

$$x=7$$

x=\frac{0±14}{2} tenglamasini yeching, bunda ± manfiy. -14 ni 2 ga bo'lish.

$$x=-7$$

Tenglama yechildi.

$$x=7 x=-7$$