(6w^2-w-5)+(4w^2-3w+2) eching

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

Baholash

$$10w^{2}-4w-3$$

Yechim qadamlari

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

$$10w^{2}-w-5-3w+2$$

-4w ni olish uchun -w va -3w ni birlashtirish.

$$10w^{2}-4w-5+2$$

-3 olish uchun -5 va 2'ni qo'shing.

$$10w^{2}-4w-3$$

Omil

$$10\left(w-\left(-\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)\left(w-\left(\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

-4w ni olish uchun -w va -3w ni birlashtirish.

$$factor(10w^{2}-4w-5+2)$$

-3 olish uchun -5 va 2'ni qo'shing.

$$factor(10w^{2}-4w-3)$$

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.

$$10w^{2}-4w-3=0$$

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.

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

-4 kvadratini chiqarish.

$$w=\frac{-\left(-4\right)±\sqrt{16-4\times 10\left(-3\right)}}{2\times 10}$$

-4 ni 10 marotabaga ko'paytirish.

$$w=\frac{-\left(-4\right)±\sqrt{16-40\left(-3\right)}}{2\times 10}$$

-40 ni -3 marotabaga ko'paytirish.

$$w=\frac{-\left(-4\right)±\sqrt{16+120}}{2\times 10}$$

16 ni 120 ga qo'shish.

$$w=\frac{-\left(-4\right)±\sqrt{136}}{2\times 10}$$

136 ning kvadrat ildizini chiqarish.

$$w=\frac{-\left(-4\right)±2\sqrt{34}}{2\times 10}$$

-4 ning teskarisi 4 ga teng.

$$w=\frac{4±2\sqrt{34}}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$w=\frac{4±2\sqrt{34}}{20}$$

w=\frac{4±2\sqrt{34}}{20} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{34} ga qo'shish.

$$w=\frac{2\sqrt{34}+4}{20}$$

4+2\sqrt{34} ni 20 ga bo'lish.

$$w=\frac{\sqrt{34}}{10}+\frac{1}{5}$$

w=\frac{4±2\sqrt{34}}{20} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{34} ni ayirish.

$$w=\frac{4-2\sqrt{34}}{20}$$

4-2\sqrt{34} ni 20 ga bo'lish.

$$w=-\frac{\sqrt{34}}{10}+\frac{1}{5}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1}{5}+\frac{\sqrt{34}}{10} ga va x_{2} uchun \frac{1}{5}-\frac{\sqrt{34}}{10} ga bo‘ling.

$$10w^{2}-4w-3=10\left(w-\left(\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)\left(w-\left(-\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)$$