x^2-48x+144 eching

$${ x }^{ 2 } -48x+144$$

Omil

$$\left(x-\left(24-12\sqrt{3}\right)\right)\left(x-\left(12\sqrt{3}+24\right)\right)$$

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.

$$x^{2}-48x+144=0$$

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.

$$x=\frac{-\left(-48\right)±\sqrt{\left(-48\right)^{2}-4\times 144}}{2}$$

-48 kvadratini chiqarish.

$$x=\frac{-\left(-48\right)±\sqrt{2304-4\times 144}}{2}$$

-4 ni 144 marotabaga ko'paytirish.

$$x=\frac{-\left(-48\right)±\sqrt{2304-576}}{2}$$

2304 ni -576 ga qo'shish.

$$x=\frac{-\left(-48\right)±\sqrt{1728}}{2}$$

1728 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-48\right)±24\sqrt{3}}{2}$$

-48 ning teskarisi 48 ga teng.

$$x=\frac{48±24\sqrt{3}}{2}$$

x=\frac{48±24\sqrt{3}}{2} tenglamasini yeching, bunda ± musbat. 48 ni 24\sqrt{3} ga qo'shish.

$$x=\frac{24\sqrt{3}+48}{2}$$

48+24\sqrt{3} ni 2 ga bo'lish.

$$x=12\sqrt{3}+24$$

x=\frac{48±24\sqrt{3}}{2} tenglamasini yeching, bunda ± manfiy. 48 dan 24\sqrt{3} ni ayirish.

$$x=\frac{48-24\sqrt{3}}{2}$$

48-24\sqrt{3} ni 2 ga bo'lish.

$$x=24-12\sqrt{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 24+12\sqrt{3} ga va x_{2} uchun 24-12\sqrt{3} ga bo‘ling.

$$x^{2}-48x+144=\left(x-\left(12\sqrt{3}+24\right)\right)\left(x-\left(24-12\sqrt{3}\right)\right)$$

Baholash

$$x^{2}-48x+144$$