x^2-16x-48 eching

$$x ^ { 2 } - 16 x - 48$$

Omil

$$\left(x-\left(8-4\sqrt{7}\right)\right)\left(x-\left(4\sqrt{7}+8\right)\right)$$

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.

$$x^{2}-16x-48=0$$

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.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-48\right)}}{2}$$

-16 kvadratini chiqarish.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\left(-48\right)}}{2}$$

-4 ni -48 marotabaga ko'paytirish.

$$x=\frac{-\left(-16\right)±\sqrt{256+192}}{2}$$

256 ni 192 ga qo'shish.

$$x=\frac{-\left(-16\right)±\sqrt{448}}{2}$$

448 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-16\right)±8\sqrt{7}}{2}$$

-16 ning teskarisi 16 ga teng.

$$x=\frac{16±8\sqrt{7}}{2}$$

x=\frac{16±8\sqrt{7}}{2} tenglamasini yeching, bunda ± musbat. 16 ni 8\sqrt{7} ga qo'shish.

$$x=\frac{8\sqrt{7}+16}{2}$$

16+8\sqrt{7} ni 2 ga bo'lish.

$$x=4\sqrt{7}+8$$

x=\frac{16±8\sqrt{7}}{2} tenglamasini yeching, bunda ± manfiy. 16 dan 8\sqrt{7} ni ayirish.

$$x=\frac{16-8\sqrt{7}}{2}$$

16-8\sqrt{7} ni 2 ga bo'lish.

$$x=8-4\sqrt{7}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 8+4\sqrt{7} ga va x_{2} uchun 8-4\sqrt{7} ga bo‘ling.

$$x^{2}-16x-48=\left(x-\left(4\sqrt{7}+8\right)\right)\left(x-\left(8-4\sqrt{7}\right)\right)$$

Baholash

$$x^{2}-16x-48$$