(-y^2-2y+3)+(-7y^2+4) eching

$$( - y ^ { 2 } - 2 y + 3 ) + ( - 7 y ^ { 2 } + 4 )$$

Baholash

$$7-2y-8y^{2}$$

Yechim qadamlari

7 olish uchun 3 va 4'ni qo'shing.

$$-y^{2}-2y+7-7y^{2}$$

-8y^{2} ni olish uchun -y^{2} va -7y^{2} ni birlashtirish.

$$-8y^{2}-2y+7$$

Omil

$$-8\left(y-\frac{-\sqrt{57}-1}{8}\right)\left(y-\frac{\sqrt{57}-1}{8}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

7 olish uchun 3 va 4'ni qo'shing.

$$factor(-y^{2}-2y+7-7y^{2})$$

-8y^{2} ni olish uchun -y^{2} va -7y^{2} ni birlashtirish.

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

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.

$$-8y^{2}-2y+7=0$$

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.

$$y=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-8\right)\times 7}}{2\left(-8\right)}$$

-2 kvadratini chiqarish.

$$y=\frac{-\left(-2\right)±\sqrt{4-4\left(-8\right)\times 7}}{2\left(-8\right)}$$

-4 ni -8 marotabaga ko'paytirish.

$$y=\frac{-\left(-2\right)±\sqrt{4+32\times 7}}{2\left(-8\right)}$$

32 ni 7 marotabaga ko'paytirish.

$$y=\frac{-\left(-2\right)±\sqrt{4+224}}{2\left(-8\right)}$$

4 ni 224 ga qo'shish.

$$y=\frac{-\left(-2\right)±\sqrt{228}}{2\left(-8\right)}$$

228 ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-2\right)±2\sqrt{57}}{2\left(-8\right)}$$

-2 ning teskarisi 2 ga teng.

$$y=\frac{2±2\sqrt{57}}{2\left(-8\right)}$$

2 ni -8 marotabaga ko'paytirish.

$$y=\frac{2±2\sqrt{57}}{-16}$$

y=\frac{2±2\sqrt{57}}{-16} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{57} ga qo'shish.

$$y=\frac{2\sqrt{57}+2}{-16}$$

2+2\sqrt{57} ni -16 ga bo'lish.

$$y=\frac{-\sqrt{57}-1}{8}$$

y=\frac{2±2\sqrt{57}}{-16} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{57} ni ayirish.

$$y=\frac{2-2\sqrt{57}}{-16}$$

2-2\sqrt{57} ni -16 ga bo'lish.

$$y=\frac{\sqrt{57}-1}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-1-\sqrt{57}}{8} ga va x_{2} uchun \frac{-1+\sqrt{57}}{8} ga bo‘ling.

$$-8y^{2}-2y+7=-8\left(y-\frac{-\sqrt{57}-1}{8}\right)\left(y-\frac{\sqrt{57}-1}{8}\right)$$