3x^2+1=28 eching

$$3 x ^ { 2 } + 1 = 28$$

x uchun yechish

$$x=3$$

$$x=-3$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 28 ni ayirish.

$$3x^{2}+1-28=0$$

-27 olish uchun 1 dan 28 ni ayirish.

$$3x^{2}-27=0$$

Ikki tarafini 3 ga bo‘ling.

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

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

Ikkala tarafdan 1 ni ayirish.

$$3x^{2}=28-1$$

27 olish uchun 28 dan 1 ni ayirish.

$$3x^{2}=27$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{27}{3}$$

9 ni olish uchun 27 ni 3 ga bo‘ling.

$$x^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=3 x=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 28 ni ayirish.

$$3x^{2}+1-28=0$$

-27 olish uchun 1 dan 28 ni ayirish.

$$3x^{2}-27=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -27 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-27\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-27\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-27\right)}}{2\times 3}$$

-12 ni -27 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{324}}{2\times 3}$$

324 ning kvadrat ildizini chiqarish.

$$x=\frac{0±18}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±18}{6}$$

x=\frac{0±18}{6} tenglamasini yeching, bunda ± musbat. 18 ni 6 ga bo'lish.

$$x=3$$

x=\frac{0±18}{6} tenglamasini yeching, bunda ± manfiy. -18 ni 6 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=3 x=-3$$