4x^2+5=1 eching

$$4 x ^ { 2 } + 5 = 1$$

x uchun yechish (complex solution)

$$x=-i$$

$$x=i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 5 ni ayirish.

$$4x^{2}=1-5$$

-4 olish uchun 1 dan 5 ni ayirish.

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

Ikki tarafini 4 ga bo‘ling.

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

-1 ni olish uchun -4 ni 4 ga bo‘ling.

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

Tenglama yechildi.

$$x=i x=-i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1 ni ayirish.

$$4x^{2}+5-1=0$$

4 olish uchun 5 dan 1 ni ayirish.

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

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 4 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\times 4}}{2\times 4}$$

-16 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-64}}{2\times 4}$$

-64 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8i}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±8i}{8}$$

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

$$x=i$$

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

$$x=-i$$

Tenglama yechildi.

$$x=i x=-i$$