frac{(4-sqrt{5})(4+sqrt{5})}{2sqrt{11}} eching

$$\frac { ( 4 - \sqrt { 5 } ) ( 4 + \sqrt { 5 } ) } { 2 \sqrt { 11 } }$$

Baholash

$$\frac{\sqrt{11}}{2}\approx 1,658312395$$

Yechim qadamlari

Hisoblang: \left(4-\sqrt{5}\right)\left(4+\sqrt{5}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{4^{2}-\left(\sqrt{5}\right)^{2}}{2\sqrt{11}}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$\frac{16-\left(\sqrt{5}\right)^{2}}{2\sqrt{11}}$$

\sqrt{5} kvadrati – 5.

$$\frac{16-5}{2\sqrt{11}}$$

11 olish uchun 16 dan 5 ni ayirish.

$$\frac{11}{2\sqrt{11}}$$

\frac{11}{2\sqrt{11}} maxrajini \sqrt{11} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{11\sqrt{11}}{2\left(\sqrt{11}\right)^{2}}$$

\sqrt{11} kvadrati – 11.

$$\frac{11\sqrt{11}}{2\times 11}$$

Surat va maxrajdagi ikkala 11 ni qisqartiring.

$$\frac{\sqrt{11}}{2}$$