4x^2+2=1 eching

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

x uchun yechish (complex solution)

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

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

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 2 ni ayirish.

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

-1 olish uchun 1 dan 2 ni ayirish.

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

Ikki tarafini 4 ga bo‘ling.

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

Tenglama yechildi.

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

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1 ni ayirish.

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

1 olish uchun 2 dan 1 ni ayirish.

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

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

$$x=\frac{0±\sqrt{0^{2}-4\times 4}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16}}{2\times 4}$$

-16 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4i}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±4i}{8}$$

x=\frac{0±4i}{8} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±4i}{8} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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