3x^2-6x+1 eching

$$3 { x }^{ 2 } -6x+1$$

Omil

$$3\left(x-\left(-\frac{\sqrt{6}}{3}+1\right)\right)\left(x-\left(\frac{\sqrt{6}}{3}+1\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$3x^{2}-6x+1=0$$

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.

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

-6 kvadratini chiqarish.

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

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-12}}{2\times 3}$$

36 ni -12 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{24}}{2\times 3}$$

24 ning kvadrat ildizini chiqarish.

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

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2\sqrt{6}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{6±2\sqrt{6}}{6}$$

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

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

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

$$x=\frac{\sqrt{6}}{3}+1$$

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

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

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

$$x=-\frac{\sqrt{6}}{3}+1$$

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

$$3x^{2}-6x+1=3\left(x-\left(\frac{\sqrt{6}}{3}+1\right)\right)\left(x-\left(-\frac{\sqrt{6}}{3}+1\right)\right)$$

Baholash

$$3x^{2}-6x+1$$