2/3+sqrt{5} eching

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

Baholash

$$\frac{3-\sqrt{5}}{2}\approx 0,381966011$$

Yechim qadamlari

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

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

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

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

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

$$\frac{2\left(3-\sqrt{5}\right)}{9-5}$$

4 olish uchun 9 dan 5 ni ayirish.

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

\frac{1}{2}\left(3-\sqrt{5}\right) ni olish uchun 2\left(3-\sqrt{5}\right) ni 4 ga bo‘ling.

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

\frac{1}{2} ga 3-\sqrt{5} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\frac{3}{2} hosil qilish uchun \frac{1}{2} va 3 ni ko'paytirish.

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

-\frac{1}{2} hosil qilish uchun \frac{1}{2} va -1 ni ko'paytirish.

$$\frac{3}{2}-\frac{1}{2}\sqrt{5}$$