x^2-1=0 eching

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

x uchun yechish

$$x=1$$

$$x=-1$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: x^{2}-1. x^{2}-1 ni x^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)=0$$

Tenglamani yechish uchun x-1=0 va x+1=0 ni yeching.

$$x=1 x=-1$$

Kvadrat ildizini topish bo'yicha qadamlar

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=1 x=-1$$

Kvadrat tenglamalaridan foydalanish qoidalari

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

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

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 -1 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-1\right)}}{2}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{4}}{2}$$

4 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2}{2}$$

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

$$x=1$$

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

$$x=-1$$

Tenglama yechildi.

$$x=1 x=-1$$