f(x)=-x^2+4x+1 eching

$$f ( x ) = - x ^ { 2 } + 4 x + 1$$

Omil

$$-\left(x-\left(2-\sqrt{5}\right)\right)\left(x-\left(\sqrt{5}+2\right)\right)$$

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.

$$-x^{2}+4x+1=0$$

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.

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

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-1\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+4}}{2\left(-1\right)}$$

16 ni 4 ga qo'shish.

$$x=\frac{-4±\sqrt{20}}{2\left(-1\right)}$$

20 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±2\sqrt{5}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±2\sqrt{5}}{-2}$$

x=\frac{-4±2\sqrt{5}}{-2} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{5} ga qo'shish.

$$x=\frac{2\sqrt{5}-4}{-2}$$

-4+2\sqrt{5} ni -2 ga bo'lish.

$$x=2-\sqrt{5}$$

x=\frac{-4±2\sqrt{5}}{-2} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{5} ni ayirish.

$$x=\frac{-2\sqrt{5}-4}{-2}$$

-4-2\sqrt{5} ni -2 ga bo'lish.

$$x=\sqrt{5}+2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 2-\sqrt{5} ga va x_{2} uchun 2+\sqrt{5} ga bo‘ling.

$$-x^{2}+4x+1=-\left(x-\left(2-\sqrt{5}\right)\right)\left(x-\left(\sqrt{5}+2\right)\right)$$

Baholash

$$1+4x-x^{2}$$