8y^2-5=0 eching

$$8 y ^ { 2 } - 5 = 0$$

y uchun yechish

$$y=\frac{\sqrt{10}}{4}\approx 0,790569415$$

$$y=-\frac{\sqrt{10}}{4}\approx -0,790569415$$

Kvadrat ildizini topish bo'yicha qadamlar

5 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$8y^{2}=5$$

Ikki tarafini 8 ga bo‘ling.

$$y^{2}=\frac{5}{8}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$y=\frac{\sqrt{10}}{4} y=-\frac{\sqrt{10}}{4}$$

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.

$$8y^{2}-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, 0 ni b va -5 ni c bilan almashtiring.

$$y=\frac{0±\sqrt{0^{2}-4\times 8\left(-5\right)}}{2\times 8}$$

0 kvadratini chiqarish.

$$y=\frac{0±\sqrt{-4\times 8\left(-5\right)}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$y=\frac{0±\sqrt{-32\left(-5\right)}}{2\times 8}$$

-32 ni -5 marotabaga ko'paytirish.

$$y=\frac{0±\sqrt{160}}{2\times 8}$$

160 ning kvadrat ildizini chiqarish.

$$y=\frac{0±4\sqrt{10}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$y=\frac{0±4\sqrt{10}}{16}$$

y=\frac{0±4\sqrt{10}}{16} tenglamasini yeching, bunda ± musbat.

$$y=\frac{\sqrt{10}}{4}$$

y=\frac{0±4\sqrt{10}}{16} tenglamasini yeching, bunda ± manfiy.

$$y=-\frac{\sqrt{10}}{4}$$

Tenglama yechildi.

$$y=\frac{\sqrt{10}}{4} y=-\frac{\sqrt{10}}{4}$$