4x^2+quad+3=0 eching

$$4 x ^ { 2 } + \quad + 3 = 0$$

x uchun yechish (complex solution)

$$x=-\frac{\sqrt{3}i}{2}\approx -0-0,866025404i$$

$$x=\frac{\sqrt{3}i}{2}\approx 0,866025404i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 3 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$4x^{2}=-3$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=-\frac{3}{4}$$

Tenglama yechildi.

$$x=\frac{\sqrt{3}i}{2} x=-\frac{\sqrt{3}i}{2}$$

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.

$$4x^{2}+3=0$$

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 3 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\times 3}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\times 3}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\times 3}}{2\times 4}$$

-16 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-48}}{2\times 4}$$

-48 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{3}i}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{3}i}{8}$$

x=\frac{0±4\sqrt{3}i}{8} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{3}i}{2}$$

x=\frac{0±4\sqrt{3}i}{8} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{3}i}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{3}i}{2} x=-\frac{\sqrt{3}i}{2}$$