(4v^2+5)+(6v^2-3v-7) eching

$$( 4 v ^ { 2 } + 5 ) + ( 6 v ^ { 2 } - 3 v - 7 )$$

Baholash

$$10v^{2}-3v-2$$

Yechim qadamlari

10v^{2} ni olish uchun 4v^{2} va 6v^{2} ni birlashtirish.

$$10v^{2}+5-3v-7$$

-2 olish uchun 5 dan 7 ni ayirish.

$$10v^{2}-2-3v$$

Omil

$$10\left(v-\frac{3-\sqrt{89}}{20}\right)\left(v-\frac{\sqrt{89}+3}{20}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

10v^{2} ni olish uchun 4v^{2} va 6v^{2} ni birlashtirish.

$$factor(10v^{2}+5-3v-7)$$

-2 olish uchun 5 dan 7 ni ayirish.

$$factor(10v^{2}-2-3v)$$

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.

$$10v^{2}-3v-2=0$$

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.

$$v=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 10\left(-2\right)}}{2\times 10}$$

-3 kvadratini chiqarish.

$$v=\frac{-\left(-3\right)±\sqrt{9-4\times 10\left(-2\right)}}{2\times 10}$$

-4 ni 10 marotabaga ko'paytirish.

$$v=\frac{-\left(-3\right)±\sqrt{9-40\left(-2\right)}}{2\times 10}$$

-40 ni -2 marotabaga ko'paytirish.

$$v=\frac{-\left(-3\right)±\sqrt{9+80}}{2\times 10}$$

9 ni 80 ga qo'shish.

$$v=\frac{-\left(-3\right)±\sqrt{89}}{2\times 10}$$

-3 ning teskarisi 3 ga teng.

$$v=\frac{3±\sqrt{89}}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$v=\frac{3±\sqrt{89}}{20}$$

v=\frac{3±\sqrt{89}}{20} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{89} ga qo'shish.

$$v=\frac{\sqrt{89}+3}{20}$$

v=\frac{3±\sqrt{89}}{20} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{89} ni ayirish.

$$v=\frac{3-\sqrt{89}}{20}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{3+\sqrt{89}}{20} ga va x_{2} uchun \frac{3-\sqrt{89}}{20} ga bo‘ling.

$$10v^{2}-3v-2=10\left(v-\frac{\sqrt{89}+3}{20}\right)\left(v-\frac{3-\sqrt{89}}{20}\right)$$