16x^2-24x+3 eching

$$16 { x }^{ 2 } -24x+3$$

Omil

$$16\left(x-\frac{3-\sqrt{6}}{4}\right)\left(x-\frac{\sqrt{6}+3}{4}\right)$$

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.

$$16x^{2}-24x+3=0$$

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.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 16\times 3}}{2\times 16}$$

-24 kvadratini chiqarish.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 16\times 3}}{2\times 16}$$

-4 ni 16 marotabaga ko'paytirish.

$$x=\frac{-\left(-24\right)±\sqrt{576-64\times 3}}{2\times 16}$$

-64 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-24\right)±\sqrt{576-192}}{2\times 16}$$

576 ni -192 ga qo'shish.

$$x=\frac{-\left(-24\right)±\sqrt{384}}{2\times 16}$$

384 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-24\right)±8\sqrt{6}}{2\times 16}$$

-24 ning teskarisi 24 ga teng.

$$x=\frac{24±8\sqrt{6}}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$x=\frac{24±8\sqrt{6}}{32}$$

x=\frac{24±8\sqrt{6}}{32} tenglamasini yeching, bunda ± musbat. 24 ni 8\sqrt{6} ga qo'shish.

$$x=\frac{8\sqrt{6}+24}{32}$$

24+8\sqrt{6} ni 32 ga bo'lish.

$$x=\frac{\sqrt{6}+3}{4}$$

x=\frac{24±8\sqrt{6}}{32} tenglamasini yeching, bunda ± manfiy. 24 dan 8\sqrt{6} ni ayirish.

$$x=\frac{24-8\sqrt{6}}{32}$$

24-8\sqrt{6} ni 32 ga bo'lish.

$$x=\frac{3-\sqrt{6}}{4}$$

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{6}}{4} ga va x_{2} uchun \frac{3-\sqrt{6}}{4} ga bo‘ling.

$$16x^{2}-24x+3=16\left(x-\frac{\sqrt{6}+3}{4}\right)\left(x-\frac{3-\sqrt{6}}{4}\right)$$

Baholash

$$16x^{2}-24x+3$$