(t^2-6t+2)+(5t^2-t-8) eching

$$( t ^ { 2 } - 6 t + 2 ) + ( 5 t ^ { 2 } - t - 8 )$$

Baholash

$$6t^{2}-7t-6$$

Yechim qadamlari

6t^{2} ni olish uchun t^{2} va 5t^{2} ni birlashtirish.

$$6t^{2}-6t+2-t-8$$

-7t ni olish uchun -6t va -t ni birlashtirish.

$$6t^{2}-7t+2-8$$

-6 olish uchun 2 dan 8 ni ayirish.

$$6t^{2}-7t-6$$

Omil

$$6\left(t-\frac{7-\sqrt{193}}{12}\right)\left(t-\frac{\sqrt{193}+7}{12}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

6t^{2} ni olish uchun t^{2} va 5t^{2} ni birlashtirish.

$$factor(6t^{2}-6t+2-t-8)$$

-7t ni olish uchun -6t va -t ni birlashtirish.

$$factor(6t^{2}-7t+2-8)$$

-6 olish uchun 2 dan 8 ni ayirish.

$$factor(6t^{2}-7t-6)$$

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.

$$6t^{2}-7t-6=0$$

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.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 6\left(-6\right)}}{2\times 6}$$

-7 kvadratini chiqarish.

$$t=\frac{-\left(-7\right)±\sqrt{49-4\times 6\left(-6\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$t=\frac{-\left(-7\right)±\sqrt{49-24\left(-6\right)}}{2\times 6}$$

-24 ni -6 marotabaga ko'paytirish.

$$t=\frac{-\left(-7\right)±\sqrt{49+144}}{2\times 6}$$

49 ni 144 ga qo'shish.

$$t=\frac{-\left(-7\right)±\sqrt{193}}{2\times 6}$$

-7 ning teskarisi 7 ga teng.

$$t=\frac{7±\sqrt{193}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$t=\frac{7±\sqrt{193}}{12}$$

t=\frac{7±\sqrt{193}}{12} tenglamasini yeching, bunda ± musbat. 7 ni \sqrt{193} ga qo'shish.

$$t=\frac{\sqrt{193}+7}{12}$$

t=\frac{7±\sqrt{193}}{12} tenglamasini yeching, bunda ± manfiy. 7 dan \sqrt{193} ni ayirish.

$$t=\frac{7-\sqrt{193}}{12}$$

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{193}}{12} ga va x_{2} uchun \frac{7-\sqrt{193}}{12} ga bo‘ling.

$$6t^{2}-7t-6=6\left(t-\frac{\sqrt{193}+7}{12}\right)\left(t-\frac{7-\sqrt{193}}{12}\right)$$