frac{5+sqrt{3}}{2-sqrt{3}} eching

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

Baholash

$$7\sqrt{3}+13\approx 25,124355653$$

Yechim qadamlari

\frac{5+\sqrt{3}}{2-\sqrt{3}} maxrajini 2+\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(5+\sqrt{3}\right)\left(2+\sqrt{3}\right)}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}$$

Hisoblang: \left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(5+\sqrt{3}\right)\left(2+\sqrt{3}\right)}{2^{2}-\left(\sqrt{3}\right)^{2}}$$

2 kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

$$\frac{\left(5+\sqrt{3}\right)\left(2+\sqrt{3}\right)}{4-3}$$

1 olish uchun 4 dan 3 ni ayirish.

$$\frac{\left(5+\sqrt{3}\right)\left(2+\sqrt{3}\right)}{1}$$

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

$$\left(5+\sqrt{3}\right)\left(2+\sqrt{3}\right)$$

5+\sqrt{3} ifodaning har bir elementini 2+\sqrt{3} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$10+5\sqrt{3}+2\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

7\sqrt{3} ni olish uchun 5\sqrt{3} va 2\sqrt{3} ni birlashtirish.

$$10+7\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$10+7\sqrt{3}+3$$

13 olish uchun 10 va 3'ni qo'shing.

$$13+7\sqrt{3}$$