36y^2+40=0 eching

$$36 { y }^{ 2 } +40 = 0$$

y uchun yechish

$$y=-\frac{\sqrt{10}i}{3}\approx -0-1,054092553i$$

$$y=\frac{\sqrt{10}i}{3}\approx 1,054092553i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 40 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$36y^{2}=-40$$

Ikki tarafini 36 ga bo‘ling.

$$y^{2}=\frac{-40}{36}$$

\frac{-40}{36} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$y^{2}=-\frac{10}{9}$$

Tenglama yechildi.

$$y=\frac{\sqrt{10}i}{3} y=-\frac{\sqrt{10}i}{3}$$

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.

$$36y^{2}+40=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 36 ni a, 0 ni b va 40 ni c bilan almashtiring.

$$y=\frac{0±\sqrt{0^{2}-4\times 36\times 40}}{2\times 36}$$

0 kvadratini chiqarish.

$$y=\frac{0±\sqrt{-4\times 36\times 40}}{2\times 36}$$

-4 ni 36 marotabaga ko'paytirish.

$$y=\frac{0±\sqrt{-144\times 40}}{2\times 36}$$

-144 ni 40 marotabaga ko'paytirish.

$$y=\frac{0±\sqrt{-5760}}{2\times 36}$$

-5760 ning kvadrat ildizini chiqarish.

$$y=\frac{0±24\sqrt{10}i}{2\times 36}$$

2 ni 36 marotabaga ko'paytirish.

$$y=\frac{0±24\sqrt{10}i}{72}$$

y=\frac{0±24\sqrt{10}i}{72} tenglamasini yeching, bunda ± musbat.

$$y=\frac{\sqrt{10}i}{3}$$

y=\frac{0±24\sqrt{10}i}{72} tenglamasini yeching, bunda ± manfiy.

$$y=-\frac{\sqrt{10}i}{3}$$

Tenglama yechildi.

$$y=\frac{\sqrt{10}i}{3} y=-\frac{\sqrt{10}i}{3}$$