frac{1-4sqrt{5}-3}{3-sqrt{5}-sqrt{5}+2}= eching

$$\frac { 1 - 4 \sqrt { 5 } - 3 } { 3 - \sqrt { 5 } - \sqrt { 5 } + 2 } =$$

Baholash

$$-\frac{24\sqrt{5}}{5}-10\approx -20,733126292$$

Yechim qadamlari

-2 olish uchun 1 dan 3 ni ayirish.

$$\frac{-2-4\sqrt{5}}{3-\sqrt{5}-\sqrt{5}+2}$$

-2\sqrt{5} ni olish uchun -\sqrt{5} va -\sqrt{5} ni birlashtirish.

$$\frac{-2-4\sqrt{5}}{3-2\sqrt{5}+2}$$

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

$$\frac{-2-4\sqrt{5}}{5-2\sqrt{5}}$$

\frac{-2-4\sqrt{5}}{5-2\sqrt{5}} maxrajini 5+2\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{\left(5-2\sqrt{5}\right)\left(5+2\sqrt{5}\right)}$$

Hisoblang: \left(5-2\sqrt{5}\right)\left(5+2\sqrt{5}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{5^{2}-\left(-2\sqrt{5}\right)^{2}}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-\left(-2\sqrt{5}\right)^{2}}$$

\left(-2\sqrt{5}\right)^{2} ni kengaytirish.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-\left(-2\right)^{2}\left(\sqrt{5}\right)^{2}}$$

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-4\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-4\times 5}$$

20 hosil qilish uchun 4 va 5 ni ko'paytirish.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-20}$$

5 olish uchun 25 dan 20 ni ayirish.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{5}$$

-2-4\sqrt{5} ifodaning har bir elementini 5+2\sqrt{5} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{-10-4\sqrt{5}-20\sqrt{5}-8\left(\sqrt{5}\right)^{2}}{5}$$

-24\sqrt{5} ni olish uchun -4\sqrt{5} va -20\sqrt{5} ni birlashtirish.

$$\frac{-10-24\sqrt{5}-8\left(\sqrt{5}\right)^{2}}{5}$$

\sqrt{5} kvadrati – 5.

$$\frac{-10-24\sqrt{5}-8\times 5}{5}$$

-40 hosil qilish uchun -8 va 5 ni ko'paytirish.

$$\frac{-10-24\sqrt{5}-40}{5}$$

-50 olish uchun -10 dan 40 ni ayirish.

$$\frac{-50-24\sqrt{5}}{5}$$