3x^2+9=0 eching

$$3 { x }^{ 2 } +9=0$$

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 9 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$3x^{2}=-9$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{-9}{3}$$

-3 ni olish uchun -9 ni 3 ga bo‘ling.

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

Tenglama yechildi.

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

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.

$$3x^{2}+9=0$$

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 9 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 9}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\times 9}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\times 9}}{2\times 3}$$

-12 ni 9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-108}}{2\times 3}$$

-108 ning kvadrat ildizini chiqarish.

$$x=\frac{0±6\sqrt{3}i}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±6\sqrt{3}i}{6}$$

x=\frac{0±6\sqrt{3}i}{6} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±6\sqrt{3}i}{6} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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