14/5sqrt{3-sqrt{5}} eching

$$\frac{ 14 }{ 5 \sqrt{ 3 } - \sqrt{ 5 } }$$

Baholash

$$\frac{\sqrt{5}\left(\sqrt{15}+1\right)}{5}\approx 2,179264403$$

Yechim qadamlari

\frac{14}{5\sqrt{3}-\sqrt{5}} maxrajini 5\sqrt{3}+\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}-\sqrt{5}\right)\left(5\sqrt{3}+\sqrt{5}\right)}$$

Hisoblang: \left(5\sqrt{3}-\sqrt{5}\right)\left(5\sqrt{3}+\sqrt{5}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

\left(5\sqrt{3}\right)^{2} ni kengaytirish.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{5^{2}\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

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

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\times 3-\left(\sqrt{5}\right)^{2}}$$

75 hosil qilish uchun 25 va 3 ni ko'paytirish.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-5}$$

70 olish uchun 75 dan 5 ni ayirish.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{70}$$

\frac{1}{5}\left(5\sqrt{3}+\sqrt{5}\right) ni olish uchun 14\left(5\sqrt{3}+\sqrt{5}\right) ni 70 ga bo‘ling.

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

\frac{1}{5} ga 5\sqrt{3}+\sqrt{5} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{5}\times 5\sqrt{3}+\frac{1}{5}\sqrt{5}$$

5 va 5 ni qisqartiring.

$$\sqrt{3}+\frac{1}{5}\sqrt{5}$$