27n^2+72-3=0 eching

$$27 n ^ { 2 } + 72 - 3 = 0$$

n uchun yechish

$$n=-\frac{\sqrt{23}i}{3}\approx -0-1,598610508i$$

$$n=\frac{\sqrt{23}i}{3}\approx 1,598610508i$$

Kvadrat ildizini topish bo'yicha qadamlar

69 olish uchun 72 dan 3 ni ayirish.

$$27n^{2}+69=0$$

Ikkala tarafdan 69 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$27n^{2}=-69$$

Ikki tarafini 27 ga bo‘ling.

$$n^{2}=\frac{-69}{27}$$

\frac{-69}{27} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$n^{2}=-\frac{23}{9}$$

Tenglama yechildi.

$$n=\frac{\sqrt{23}i}{3} n=-\frac{\sqrt{23}i}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

69 olish uchun 72 dan 3 ni ayirish.

$$27n^{2}+69=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 27 ni a, 0 ni b va 69 ni c bilan almashtiring.

$$n=\frac{0±\sqrt{0^{2}-4\times 27\times 69}}{2\times 27}$$

0 kvadratini chiqarish.

$$n=\frac{0±\sqrt{-4\times 27\times 69}}{2\times 27}$$

-4 ni 27 marotabaga ko'paytirish.

$$n=\frac{0±\sqrt{-108\times 69}}{2\times 27}$$

-108 ni 69 marotabaga ko'paytirish.

$$n=\frac{0±\sqrt{-7452}}{2\times 27}$$

-7452 ning kvadrat ildizini chiqarish.

$$n=\frac{0±18\sqrt{23}i}{2\times 27}$$

2 ni 27 marotabaga ko'paytirish.

$$n=\frac{0±18\sqrt{23}i}{54}$$

n=\frac{0±18\sqrt{23}i}{54} tenglamasini yeching, bunda ± musbat.

$$n=\frac{\sqrt{23}i}{3}$$

n=\frac{0±18\sqrt{23}i}{54} tenglamasini yeching, bunda ± manfiy.

$$n=-\frac{\sqrt{23}i}{3}$$

Tenglama yechildi.

$$n=\frac{\sqrt{23}i}{3} n=-\frac{\sqrt{23}i}{3}$$