8x^2+3-4x-5x^2-9x eching

$$8 { x }^{ 2 } +3-4x-5 { x }^{ 2 } -9x$$

Baholash

$$3x^{2}-13x+3$$

Yechim qadamlari

3x^{2} ni olish uchun 8x^{2} va -5x^{2} ni birlashtirish.

$$3x^{2}+3-4x-9x$$

-13x ni olish uchun -4x va -9x ni birlashtirish.

$$3x^{2}+3-13x$$

Omil

$$3\left(x-\frac{13-\sqrt{133}}{6}\right)\left(x-\frac{\sqrt{133}+13}{6}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x^{2} ni olish uchun 8x^{2} va -5x^{2} ni birlashtirish.

$$factor(3x^{2}+3-4x-9x)$$

-13x ni olish uchun -4x va -9x ni birlashtirish.

$$factor(3x^{2}+3-13x)$$

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.

$$3x^{2}-13x+3=0$$

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.

$$x=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 3\times 3}}{2\times 3}$$

-13 kvadratini chiqarish.

$$x=\frac{-\left(-13\right)±\sqrt{169-4\times 3\times 3}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-13\right)±\sqrt{169-12\times 3}}{2\times 3}$$

-12 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-13\right)±\sqrt{169-36}}{2\times 3}$$

169 ni -36 ga qo'shish.

$$x=\frac{-\left(-13\right)±\sqrt{133}}{2\times 3}$$

-13 ning teskarisi 13 ga teng.

$$x=\frac{13±\sqrt{133}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{13±\sqrt{133}}{6}$$

x=\frac{13±\sqrt{133}}{6} tenglamasini yeching, bunda ± musbat. 13 ni \sqrt{133} ga qo'shish.

$$x=\frac{\sqrt{133}+13}{6}$$

x=\frac{13±\sqrt{133}}{6} tenglamasini yeching, bunda ± manfiy. 13 dan \sqrt{133} ni ayirish.

$$x=\frac{13-\sqrt{133}}{6}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{13+\sqrt{133}}{6} ga va x_{2} uchun \frac{13-\sqrt{133}}{6} ga bo‘ling.

$$3x^{2}-13x+3=3\left(x-\frac{\sqrt{133}+13}{6}\right)\left(x-\frac{13-\sqrt{133}}{6}\right)$$