frac{2-sqrt{5}}{sqrt{5}+2} eching

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

Baholash

$$4\sqrt{5}-9\approx -0,05572809$$

Yechim qadamlari

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

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

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

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

\sqrt{5} kvadratini chiqarish. 2 kvadratini chiqarish.

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

1 olish uchun 5 dan 4 ni ayirish.

$$\frac{\left(2-\sqrt{5}\right)\left(\sqrt{5}-2\right)}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

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

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

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

\sqrt{5} kvadrati – 5.

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

-9 olish uchun -4 dan 5 ni ayirish.

$$2\sqrt{5}-9+2\sqrt{5}$$

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

$$4\sqrt{5}-9$$