x^2+4x+2+x^2-4 eching

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

Baholash

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

Yechim qadamlari

2x^{2} ni olish uchun x^{2} va x^{2} ni birlashtirish.

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

-2 olish uchun 2 dan 4 ni ayirish.

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

Omil

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

Kvadrat tenglamalaridan foydalanish qoidalari

2x^{2} ni olish uchun x^{2} va x^{2} ni birlashtirish.

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

-2 olish uchun 2 dan 4 ni ayirish.

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

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.

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

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.

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

4 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-8\left(-2\right)}}{2\times 2}$$

-8 ni -2 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+16}}{2\times 2}$$

16 ni 16 ga qo'shish.

$$x=\frac{-4±\sqrt{32}}{2\times 2}$$

32 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4\sqrt{2}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-4±4\sqrt{2}}{4}$$

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

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

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

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

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

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

-4-4\sqrt{2} ni 4 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.

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