6y^2-21y+12 eching

$$6 y ^ { 2 } - 21 y + 12$$

Omil

$$6\left(y-\frac{7-\sqrt{17}}{4}\right)\left(y-\frac{\sqrt{17}+7}{4}\right)$$

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.

$$6y^{2}-21y+12=0$$

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.

$$y=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\times 6\times 12}}{2\times 6}$$

-21 kvadratini chiqarish.

$$y=\frac{-\left(-21\right)±\sqrt{441-4\times 6\times 12}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$y=\frac{-\left(-21\right)±\sqrt{441-24\times 12}}{2\times 6}$$

-24 ni 12 marotabaga ko'paytirish.

$$y=\frac{-\left(-21\right)±\sqrt{441-288}}{2\times 6}$$

441 ni -288 ga qo'shish.

$$y=\frac{-\left(-21\right)±\sqrt{153}}{2\times 6}$$

153 ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-21\right)±3\sqrt{17}}{2\times 6}$$

-21 ning teskarisi 21 ga teng.

$$y=\frac{21±3\sqrt{17}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$y=\frac{21±3\sqrt{17}}{12}$$

y=\frac{21±3\sqrt{17}}{12} tenglamasini yeching, bunda ± musbat. 21 ni 3\sqrt{17} ga qo'shish.

$$y=\frac{3\sqrt{17}+21}{12}$$

21+3\sqrt{17} ni 12 ga bo'lish.

$$y=\frac{\sqrt{17}+7}{4}$$

y=\frac{21±3\sqrt{17}}{12} tenglamasini yeching, bunda ± manfiy. 21 dan 3\sqrt{17} ni ayirish.

$$y=\frac{21-3\sqrt{17}}{12}$$

21-3\sqrt{17} ni 12 ga bo'lish.

$$y=\frac{7-\sqrt{17}}{4}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{7+\sqrt{17}}{4} ga va x_{2} uchun \frac{7-\sqrt{17}}{4} ga bo‘ling.

$$6y^{2}-21y+12=6\left(y-\frac{\sqrt{17}+7}{4}\right)\left(y-\frac{7-\sqrt{17}}{4}\right)$$

Baholash

$$6y^{2}-21y+12$$