2x-3x^2+2x+1 eching

$$2 x - 3 x ^ { 2 } + 2 x + 1$$

Omil

$$-3\left(x-\frac{2-\sqrt{7}}{3}\right)\left(x-\frac{\sqrt{7}+2}{3}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

4x ni olish uchun 2x va 2x ni birlashtirish.

$$factor(4x-3x^{2}+1)$$

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.

$$-3x^{2}+4x+1=0$$

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.

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

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-3\right)}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+12}}{2\left(-3\right)}$$

16 ni 12 ga qo'shish.

$$x=\frac{-4±\sqrt{28}}{2\left(-3\right)}$$

28 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±2\sqrt{7}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{-4±2\sqrt{7}}{-6}$$

x=\frac{-4±2\sqrt{7}}{-6} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{7} ga qo'shish.

$$x=\frac{2\sqrt{7}-4}{-6}$$

-4+2\sqrt{7} ni -6 ga bo'lish.

$$x=\frac{2-\sqrt{7}}{3}$$

x=\frac{-4±2\sqrt{7}}{-6} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{7} ni ayirish.

$$x=\frac{-2\sqrt{7}-4}{-6}$$

-4-2\sqrt{7} ni -6 ga bo'lish.

$$x=\frac{\sqrt{7}+2}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{2-\sqrt{7}}{3} ga va x_{2} uchun \frac{2+\sqrt{7}}{3} ga bo‘ling.

$$-3x^{2}+4x+1=-3\left(x-\frac{2-\sqrt{7}}{3}\right)\left(x-\frac{\sqrt{7}+2}{3}\right)$$

Baholash

$$1+4x-3x^{2}$$

Yechim qadamlari

4x ni olish uchun 2x va 2x ni birlashtirish.

$$4x-3x^{2}+1$$