2a^2+8a-13+3a^2-11a-5 eching

$$2 a ^ { 2 } + 8 a - 13 + 3 a ^ { 2 } - 11 a - 5$$

Baholash

$$5a^{2}-3a-18$$

Yechim qadamlari

5a^{2} ni olish uchun 2a^{2} va 3a^{2} ni birlashtirish.

$$5a^{2}+8a-13-11a-5$$

-3a ni olish uchun 8a va -11a ni birlashtirish.

$$5a^{2}-3a-13-5$$

-18 olish uchun -13 dan 5 ni ayirish.

$$5a^{2}-3a-18$$

Omil

$$5\left(a-\frac{3-3\sqrt{41}}{10}\right)\left(a-\frac{3\sqrt{41}+3}{10}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

5a^{2} ni olish uchun 2a^{2} va 3a^{2} ni birlashtirish.

$$factor(5a^{2}+8a-13-11a-5)$$

-3a ni olish uchun 8a va -11a ni birlashtirish.

$$factor(5a^{2}-3a-13-5)$$

-18 olish uchun -13 dan 5 ni ayirish.

$$factor(5a^{2}-3a-18)$$

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.

$$5a^{2}-3a-18=0$$

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.

$$a=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 5\left(-18\right)}}{2\times 5}$$

-3 kvadratini chiqarish.

$$a=\frac{-\left(-3\right)±\sqrt{9-4\times 5\left(-18\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$a=\frac{-\left(-3\right)±\sqrt{9-20\left(-18\right)}}{2\times 5}$$

-20 ni -18 marotabaga ko'paytirish.

$$a=\frac{-\left(-3\right)±\sqrt{9+360}}{2\times 5}$$

9 ni 360 ga qo'shish.

$$a=\frac{-\left(-3\right)±\sqrt{369}}{2\times 5}$$

369 ning kvadrat ildizini chiqarish.

$$a=\frac{-\left(-3\right)±3\sqrt{41}}{2\times 5}$$

-3 ning teskarisi 3 ga teng.

$$a=\frac{3±3\sqrt{41}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$a=\frac{3±3\sqrt{41}}{10}$$

a=\frac{3±3\sqrt{41}}{10} tenglamasini yeching, bunda ± musbat. 3 ni 3\sqrt{41} ga qo'shish.

$$a=\frac{3\sqrt{41}+3}{10}$$

a=\frac{3±3\sqrt{41}}{10} tenglamasini yeching, bunda ± manfiy. 3 dan 3\sqrt{41} ni ayirish.

$$a=\frac{3-3\sqrt{41}}{10}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{3+3\sqrt{41}}{10} ga va x_{2} uchun \frac{3-3\sqrt{41}}{10} ga bo‘ling.

$$5a^{2}-3a-18=5\left(a-\frac{3\sqrt{41}+3}{10}\right)\left(a-\frac{3-3\sqrt{41}}{10}\right)$$