2/sqrt{7+5} eching

$$\frac{ 2 }{ \sqrt{ 7 } +5 }$$

Baholash

$$\frac{5-\sqrt{7}}{9}\approx 0,261583188$$

Yechim qadamlari

\frac{2}{\sqrt{7}+5} maxrajini \sqrt{7}-5 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\left(\sqrt{7}-5\right)}{\left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right)}$$

Hisoblang: \left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(\sqrt{7}-5\right)}{\left(\sqrt{7}\right)^{2}-5^{2}}$$

\sqrt{7} kvadratini chiqarish. 5 kvadratini chiqarish.

$$\frac{2\left(\sqrt{7}-5\right)}{7-25}$$

-18 olish uchun 7 dan 25 ni ayirish.

$$\frac{2\left(\sqrt{7}-5\right)}{-18}$$

-\frac{1}{9}\left(\sqrt{7}-5\right) ni olish uchun 2\left(\sqrt{7}-5\right) ni -18 ga bo‘ling.

$$-\frac{1}{9}\left(\sqrt{7}-5\right)$$

-\frac{1}{9} ga \sqrt{7}-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-\frac{1}{9}\sqrt{7}-\frac{1}{9}\left(-5\right)$$

-\frac{1}{9}\left(-5\right) ni yagona kasrga aylantiring.

$$-\frac{1}{9}\sqrt{7}+\frac{-\left(-5\right)}{9}$$

5 hosil qilish uchun -1 va -5 ni ko'paytirish.

$$-\frac{1}{9}\sqrt{7}+\frac{5}{9}$$