x^2-3x-2 eching

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

Omil

$$\left(x-\frac{3-\sqrt{17}}{2}\right)\left(x-\frac{\sqrt{17}+3}{2}\right)$$

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.

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

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.

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

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-2\right)}}{2}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+8}}{2}$$

9 ni 8 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{17}}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±\sqrt{17}}{2}$$

x=\frac{3±\sqrt{17}}{2} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{17} ga qo'shish.

$$x=\frac{\sqrt{17}+3}{2}$$

x=\frac{3±\sqrt{17}}{2} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{17} ni ayirish.

$$x=\frac{3-\sqrt{17}}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{3+\sqrt{17}}{2} ga va x_{2} uchun \frac{3-\sqrt{17}}{2} ga bo‘ling.

$$x^{2}-3x-2=\left(x-\frac{\sqrt{17}+3}{2}\right)\left(x-\frac{3-\sqrt{17}}{2}\right)$$

Baholash

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