x^2-3=1 eching

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

x uchun yechish

$$x=2$$

$$x=-2$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 1 ni ayirish.

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

-4 olish uchun -3 dan 1 ni ayirish.

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

Hisoblang: x^{2}-4. x^{2}-4 ni x^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)=0$$

Tenglamani yechish uchun x-2=0 va x+2=0 ni yeching.

$$x=2 x=-2$$

Kvadrat ildizini topish bo'yicha qadamlar

3 ni ikki tarafga qo’shing.

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

4 olish uchun 1 va 3'ni qo'shing.

$$x^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2 x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1 ni ayirish.

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

-4 olish uchun -3 dan 1 ni ayirish.

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

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 -4 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16}}{2}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4}{2}$$

x=\frac{0±4}{2} tenglamasini yeching, bunda ± musbat. 4 ni 2 ga bo'lish.

$$x=2$$

x=\frac{0±4}{2} tenglamasini yeching, bunda ± manfiy. -4 ni 2 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

$$x=2 x=-2$$