72n^2-16n-8 eching

$$72 { n }^{ 2 } -16n-8$$

Omil

$$72\left(n-\frac{1-\sqrt{10}}{9}\right)\left(n-\frac{\sqrt{10}+1}{9}\right)$$

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.

$$72n^{2}-16n-8=0$$

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.

$$n=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 72\left(-8\right)}}{2\times 72}$$

-16 kvadratini chiqarish.

$$n=\frac{-\left(-16\right)±\sqrt{256-4\times 72\left(-8\right)}}{2\times 72}$$

-4 ni 72 marotabaga ko'paytirish.

$$n=\frac{-\left(-16\right)±\sqrt{256-288\left(-8\right)}}{2\times 72}$$

-288 ni -8 marotabaga ko'paytirish.

$$n=\frac{-\left(-16\right)±\sqrt{256+2304}}{2\times 72}$$

256 ni 2304 ga qo'shish.

$$n=\frac{-\left(-16\right)±\sqrt{2560}}{2\times 72}$$

2560 ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-16\right)±16\sqrt{10}}{2\times 72}$$

-16 ning teskarisi 16 ga teng.

$$n=\frac{16±16\sqrt{10}}{2\times 72}$$

2 ni 72 marotabaga ko'paytirish.

$$n=\frac{16±16\sqrt{10}}{144}$$

n=\frac{16±16\sqrt{10}}{144} tenglamasini yeching, bunda ± musbat. 16 ni 16\sqrt{10} ga qo'shish.

$$n=\frac{16\sqrt{10}+16}{144}$$

16+16\sqrt{10} ni 144 ga bo'lish.

$$n=\frac{\sqrt{10}+1}{9}$$

n=\frac{16±16\sqrt{10}}{144} tenglamasini yeching, bunda ± manfiy. 16 dan 16\sqrt{10} ni ayirish.

$$n=\frac{16-16\sqrt{10}}{144}$$

16-16\sqrt{10} ni 144 ga bo'lish.

$$n=\frac{1-\sqrt{10}}{9}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1+\sqrt{10}}{9} ga va x_{2} uchun \frac{1-\sqrt{10}}{9} ga bo‘ling.

$$72n^{2}-16n-8=72\left(n-\frac{\sqrt{10}+1}{9}\right)\left(n-\frac{1-\sqrt{10}}{9}\right)$$

Baholash

$$72n^{2}-16n-8$$