5=y^2-8 eching

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

y uchun yechish

$$y=\sqrt{13}\approx 3,605551275$$

$$y=-\sqrt{13}\approx -3,605551275$$

Kvadrat ildizini topish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

8 ni ikki tarafga qo’shing.

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

13 olish uchun 5 va 8'ni qo'shing.

$$y^{2}=13$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$y=\sqrt{13} y=-\sqrt{13}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

Ikkala tarafdan 5 ni ayirish.

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

-13 olish uchun -8 dan 5 ni ayirish.

$$y^{2}-13=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -13 ni c bilan almashtiring.

$$y=\frac{0±\sqrt{0^{2}-4\left(-13\right)}}{2}$$

0 kvadratini chiqarish.

$$y=\frac{0±\sqrt{-4\left(-13\right)}}{2}$$

-4 ni -13 marotabaga ko'paytirish.

$$y=\frac{0±\sqrt{52}}{2}$$

52 ning kvadrat ildizini chiqarish.

$$y=\frac{0±2\sqrt{13}}{2}$$

y=\frac{0±2\sqrt{13}}{2} tenglamasini yeching, bunda ± musbat.

$$y=\sqrt{13}$$

y=\frac{0±2\sqrt{13}}{2} tenglamasini yeching, bunda ± manfiy.

$$y=-\sqrt{13}$$

Tenglama yechildi.

$$y=\sqrt{13} y=-\sqrt{13}$$