65y^2-23y-10 eching

$$65 y ^ { 2 } - 23 y - 10$$

Omil

$$65\left(y-\frac{23-\sqrt{3129}}{130}\right)\left(y-\frac{\sqrt{3129}+23}{130}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$65y^{2}-23y-10=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$y=\frac{-\left(-23\right)±\sqrt{\left(-23\right)^{2}-4\times 65\left(-10\right)}}{2\times 65}$$

-23 kvadratini chiqarish.

$$y=\frac{-\left(-23\right)±\sqrt{529-4\times 65\left(-10\right)}}{2\times 65}$$

-4 ni 65 marotabaga ko'paytirish.

$$y=\frac{-\left(-23\right)±\sqrt{529-260\left(-10\right)}}{2\times 65}$$

-260 ni -10 marotabaga ko'paytirish.

$$y=\frac{-\left(-23\right)±\sqrt{529+2600}}{2\times 65}$$

529 ni 2600 ga qo'shish.

$$y=\frac{-\left(-23\right)±\sqrt{3129}}{2\times 65}$$

-23 ning teskarisi 23 ga teng.

$$y=\frac{23±\sqrt{3129}}{2\times 65}$$

2 ni 65 marotabaga ko'paytirish.

$$y=\frac{23±\sqrt{3129}}{130}$$

y=\frac{23±\sqrt{3129}}{130} tenglamasini yeching, bunda ± musbat. 23 ni \sqrt{3129} ga qo'shish.

$$y=\frac{\sqrt{3129}+23}{130}$$

y=\frac{23±\sqrt{3129}}{130} tenglamasini yeching, bunda ± manfiy. 23 dan \sqrt{3129} ni ayirish.

$$y=\frac{23-\sqrt{3129}}{130}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{23+\sqrt{3129}}{130} ga va x_{2} uchun \frac{23-\sqrt{3129}}{130} ga bo‘ling.

$$65y^{2}-23y-10=65\left(y-\frac{\sqrt{3129}+23}{130}\right)\left(y-\frac{23-\sqrt{3129}}{130}\right)$$

Baholash

$$65y^{2}-23y-10$$