(11n^2+2n-8)+(4n^2-5n+7) eching

$$( 11 n ^ { 2 } + 2 n - 8 ) + ( 4 n ^ { 2 } - 5 n + 7 )$$

Baholash

$$15n^{2}-3n-1$$

Yechim qadamlari

15n^{2} ni olish uchun 11n^{2} va 4n^{2} ni birlashtirish.

$$15n^{2}+2n-8-5n+7$$

-3n ni olish uchun 2n va -5n ni birlashtirish.

$$15n^{2}-3n-8+7$$

-1 olish uchun -8 va 7'ni qo'shing.

$$15n^{2}-3n-1$$

Omil

$$15\left(n-\left(-\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)\left(n-\left(\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

15n^{2} ni olish uchun 11n^{2} va 4n^{2} ni birlashtirish.

$$factor(15n^{2}+2n-8-5n+7)$$

-3n ni olish uchun 2n va -5n ni birlashtirish.

$$factor(15n^{2}-3n-8+7)$$

-1 olish uchun -8 va 7'ni qo'shing.

$$factor(15n^{2}-3n-1)$$

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.

$$15n^{2}-3n-1=0$$

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.

$$n=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 15\left(-1\right)}}{2\times 15}$$

-3 kvadratini chiqarish.

$$n=\frac{-\left(-3\right)±\sqrt{9-4\times 15\left(-1\right)}}{2\times 15}$$

-4 ni 15 marotabaga ko'paytirish.

$$n=\frac{-\left(-3\right)±\sqrt{9-60\left(-1\right)}}{2\times 15}$$

-60 ni -1 marotabaga ko'paytirish.

$$n=\frac{-\left(-3\right)±\sqrt{9+60}}{2\times 15}$$

9 ni 60 ga qo'shish.

$$n=\frac{-\left(-3\right)±\sqrt{69}}{2\times 15}$$

-3 ning teskarisi 3 ga teng.

$$n=\frac{3±\sqrt{69}}{2\times 15}$$

2 ni 15 marotabaga ko'paytirish.

$$n=\frac{3±\sqrt{69}}{30}$$

n=\frac{3±\sqrt{69}}{30} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{69} ga qo'shish.

$$n=\frac{\sqrt{69}+3}{30}$$

3+\sqrt{69} ni 30 ga bo'lish.

$$n=\frac{\sqrt{69}}{30}+\frac{1}{10}$$

n=\frac{3±\sqrt{69}}{30} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{69} ni ayirish.

$$n=\frac{3-\sqrt{69}}{30}$$

3-\sqrt{69} ni 30 ga bo'lish.

$$n=-\frac{\sqrt{69}}{30}+\frac{1}{10}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1}{10}+\frac{\sqrt{69}}{30} ga va x_{2} uchun \frac{1}{10}-\frac{\sqrt{69}}{30} ga bo‘ling.

$$15n^{2}-3n-1=15\left(n-\left(\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)\left(n-\left(-\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)$$