80*y+20+8*y^2 eching

$$80 \cdot y + 20 + 8 \cdot y ^ { 2 }$$

Omil

$$8\left(y-\left(-\frac{3\sqrt{10}}{2}-5\right)\right)\left(y-\left(\frac{3\sqrt{10}}{2}-5\right)\right)$$

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.

$$8y^{2}+80y+20=0$$

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.

$$y=\frac{-80±\sqrt{80^{2}-4\times 8\times 20}}{2\times 8}$$

80 kvadratini chiqarish.

$$y=\frac{-80±\sqrt{6400-4\times 8\times 20}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$y=\frac{-80±\sqrt{6400-32\times 20}}{2\times 8}$$

-32 ni 20 marotabaga ko'paytirish.

$$y=\frac{-80±\sqrt{6400-640}}{2\times 8}$$

6400 ni -640 ga qo'shish.

$$y=\frac{-80±\sqrt{5760}}{2\times 8}$$

5760 ning kvadrat ildizini chiqarish.

$$y=\frac{-80±24\sqrt{10}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$y=\frac{-80±24\sqrt{10}}{16}$$

y=\frac{-80±24\sqrt{10}}{16} tenglamasini yeching, bunda ± musbat. -80 ni 24\sqrt{10} ga qo'shish.

$$y=\frac{24\sqrt{10}-80}{16}$$

-80+24\sqrt{10} ni 16 ga bo'lish.

$$y=\frac{3\sqrt{10}}{2}-5$$

y=\frac{-80±24\sqrt{10}}{16} tenglamasini yeching, bunda ± manfiy. -80 dan 24\sqrt{10} ni ayirish.

$$y=\frac{-24\sqrt{10}-80}{16}$$

-80-24\sqrt{10} ni 16 ga bo'lish.

$$y=-\frac{3\sqrt{10}}{2}-5$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -5+\frac{3\sqrt{10}}{2} ga va x_{2} uchun -5-\frac{3\sqrt{10}}{2} ga bo‘ling.

$$8y^{2}+80y+20=8\left(y-\left(\frac{3\sqrt{10}}{2}-5\right)\right)\left(y-\left(-\frac{3\sqrt{10}}{2}-5\right)\right)$$

Baholash

$$8y^{2}+80y+20$$