4x^2=1 eching

$$4 { x }^{ 2 } =1$$

x uchun yechish

$$x=\frac{1}{2}=0,5$$

$$x=-\frac{1}{2}=-0,5$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{1}{4}$$

Ikkala tarafdan \frac{1}{4} ni ayirish.

$$x^{2}-\frac{1}{4}=0$$

Ikkala tarafini 4 ga ko‘paytiring.

$$4x^{2}-1=0$$

Hisoblang: 4x^{2}-1. 4x^{2}-1 ni \left(2x\right)^{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).

$$\left(2x-1\right)\left(2x+1\right)=0$$

Tenglamani yechish uchun 2x-1=0 va 2x+1=0 ni yeching.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{1}{4}$$

Ikkala tarafdan \frac{1}{4} ni ayirish.

$$x^{2}-\frac{1}{4}=0$$

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 -\frac{1}{4} ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -\frac{1}{4} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1}}{2}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{0±1}{2}$$

x=\frac{0±1}{2} tenglamasini yeching, bunda ± musbat. 1 ni 2 ga bo'lish.

$$x=\frac{1}{2}$$

x=\frac{0±1}{2} tenglamasini yeching, bunda ± manfiy. -1 ni 2 ga bo'lish.

$$x=-\frac{1}{2}$$

Tenglama yechildi.

$$x=\frac{1}{2} x=-\frac{1}{2}$$