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

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

Baholash

$$4\sqrt{3}+7\approx 13,92820323$$

Yechim qadamlari

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

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

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}.

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

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

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

1 olish uchun 4 dan 3 ni ayirish.

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

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

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

\left(2+\sqrt{3}\right)^{2} hosil qilish uchun 2+\sqrt{3} va 2+\sqrt{3} ni ko'paytirish.

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

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2+\sqrt{3}\right)^{2} kengaytirilishi uchun ishlating.

$$4+4\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$4+4\sqrt{3}+3$$

7 olish uchun 4 va 3'ni qo'shing.

$$7+4\sqrt{3}$$