f(x)=x^2+2x-1 eching

$$f ( x ) = x ^ { 2 } + 2 x - 1$$

Omil

$$\left(x-\left(-\sqrt{2}-1\right)\right)\left(x-\left(\sqrt{2}-1\right)\right)$$

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.

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

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.

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

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\left(-1\right)}}{2}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+4}}{2}$$

4 ni 4 ga qo'shish.

$$x=\frac{-2±\sqrt{8}}{2}$$

8 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{2}}{2}$$

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

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

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

$$x=\sqrt{2}-1$$

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

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

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

$$x=-\sqrt{2}-1$$

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

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

Baholash

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