3x^2+55=0 eching

$$3 x ^ { 2 } + 55 = 0$$

x uchun yechish (complex solution)

$$x=-\frac{\sqrt{165}i}{3}\approx -0-4,281744193i$$

$$x=\frac{\sqrt{165}i}{3}\approx 4,281744193i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 55 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$3x^{2}=-55$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=-\frac{55}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{165}i}{3} x=-\frac{\sqrt{165}i}{3}$$

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.

$$3x^{2}+55=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va 55 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 55}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\times 55}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\times 55}}{2\times 3}$$

-12 ni 55 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-660}}{2\times 3}$$

-660 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{165}i}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{165}i}{6}$$

x=\frac{0±2\sqrt{165}i}{6} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{165}i}{3}$$

x=\frac{0±2\sqrt{165}i}{6} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{165}i}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{165}i}{3} x=-\frac{\sqrt{165}i}{3}$$