5x^2-7x+x-3 eching

$$5 x ^ { 2 } - 7 x + x - 3$$

Omil

$$5\left(x-\frac{3-2\sqrt{6}}{5}\right)\left(x-\frac{2\sqrt{6}+3}{5}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-6x ni olish uchun -7x va x ni birlashtirish.

$$factor(5x^{2}-6x-3)$$

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.

$$5x^{2}-6x-3=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 5\left(-3\right)}}{2\times 5}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 5\left(-3\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-20\left(-3\right)}}{2\times 5}$$

-20 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+60}}{2\times 5}$$

36 ni 60 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{96}}{2\times 5}$$

96 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±4\sqrt{6}}{2\times 5}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±4\sqrt{6}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{6±4\sqrt{6}}{10}$$

x=\frac{6±4\sqrt{6}}{10} tenglamasini yeching, bunda ± musbat. 6 ni 4\sqrt{6} ga qo'shish.

$$x=\frac{4\sqrt{6}+6}{10}$$

6+4\sqrt{6} ni 10 ga bo'lish.

$$x=\frac{2\sqrt{6}+3}{5}$$

x=\frac{6±4\sqrt{6}}{10} tenglamasini yeching, bunda ± manfiy. 6 dan 4\sqrt{6} ni ayirish.

$$x=\frac{6-4\sqrt{6}}{10}$$

6-4\sqrt{6} ni 10 ga bo'lish.

$$x=\frac{3-2\sqrt{6}}{5}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{3+2\sqrt{6}}{5} ga va x_{2} uchun \frac{3-2\sqrt{6}}{5} ga bo‘ling.

$$5x^{2}-6x-3=5\left(x-\frac{2\sqrt{6}+3}{5}\right)\left(x-\frac{3-2\sqrt{6}}{5}\right)$$

Baholash

$$5x^{2}-6x-3$$

Yechim qadamlari

-6x ni olish uchun -7x va x ni birlashtirish.

$$5x^{2}-6x-3$$