6u^2+24u-36 eching

$$6 u ^ { 2 } + 24 u - 36$$

Omil

$$6\left(u-\left(-\sqrt{10}-2\right)\right)\left(u-\left(\sqrt{10}-2\right)\right)$$

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.

$$6u^{2}+24u-36=0$$

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.

$$u=\frac{-24±\sqrt{24^{2}-4\times 6\left(-36\right)}}{2\times 6}$$

24 kvadratini chiqarish.

$$u=\frac{-24±\sqrt{576-4\times 6\left(-36\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$u=\frac{-24±\sqrt{576-24\left(-36\right)}}{2\times 6}$$

-24 ni -36 marotabaga ko'paytirish.

$$u=\frac{-24±\sqrt{576+864}}{2\times 6}$$

576 ni 864 ga qo'shish.

$$u=\frac{-24±\sqrt{1440}}{2\times 6}$$

1440 ning kvadrat ildizini chiqarish.

$$u=\frac{-24±12\sqrt{10}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$u=\frac{-24±12\sqrt{10}}{12}$$

u=\frac{-24±12\sqrt{10}}{12} tenglamasini yeching, bunda ± musbat. -24 ni 12\sqrt{10} ga qo'shish.

$$u=\frac{12\sqrt{10}-24}{12}$$

-24+12\sqrt{10} ni 12 ga bo'lish.

$$u=\sqrt{10}-2$$

u=\frac{-24±12\sqrt{10}}{12} tenglamasini yeching, bunda ± manfiy. -24 dan 12\sqrt{10} ni ayirish.

$$u=\frac{-12\sqrt{10}-24}{12}$$

-24-12\sqrt{10} ni 12 ga bo'lish.

$$u=-\sqrt{10}-2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -2+\sqrt{10} ga va x_{2} uchun -2-\sqrt{10} ga bo‘ling.

$$6u^{2}+24u-36=6\left(u-\left(\sqrt{10}-2\right)\right)\left(u-\left(-\sqrt{10}-2\right)\right)$$

Baholash

$$6\left(u^{2}+4u-6\right)$$