2x^2+7=1 eching

$$2 x ^ { 2 } + 7 = 1$$

x uchun yechish (complex solution)

$$x=-\sqrt{3}i\approx -0-1,732050808i$$

$$x=\sqrt{3}i\approx 1,732050808i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 7 ni ayirish.

$$2x^{2}=1-7$$

-6 olish uchun 1 dan 7 ni ayirish.

$$2x^{2}=-6$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{-6}{2}$$

-3 ni olish uchun -6 ni 2 ga bo‘ling.

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

Tenglama yechildi.

$$x=\sqrt{3}i x=-\sqrt{3}i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1 ni ayirish.

$$2x^{2}+7-1=0$$

6 olish uchun 7 dan 1 ni ayirish.

$$2x^{2}+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 0 ni b va 6 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 6}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\times 6}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\times 6}}{2\times 2}$$

-8 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-48}}{2\times 2}$$

-48 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{3}i}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{3}i}{4}$$

x=\frac{0±4\sqrt{3}i}{4} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{3}i$$

x=\frac{0±4\sqrt{3}i}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{3}i$$

Tenglama yechildi.

$$x=\sqrt{3}i x=-\sqrt{3}i$$