3-frac{sqrt{2}}{(1-sqrt{5}} eching

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

Baholash

$$\frac{\sqrt{2}+\sqrt{10}+12}{4}\approx 4,144122806$$

Qisqa yechim qadamlari

\frac{\sqrt{2}}{1-\sqrt{5}} maxrajini 1+\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

Hisoblang: \left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

-4 olish uchun 1 dan 5 ni ayirish.

$$3-\frac{\sqrt{2}\left(1+\sqrt{5}\right)}{-4}$$

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

$$3-\frac{\sqrt{2}+\sqrt{2}\sqrt{5}}{-4}$$

\sqrt{2} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$3-\frac{\sqrt{2}+\sqrt{10}}{-4}$$

Surat va maxrajini -1 ga ko‘paytiring.

$$3-\frac{-\sqrt{2}-\sqrt{10}}{4}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 ni \frac{4}{4} marotabaga ko'paytirish.

$$\frac{3\times 4}{4}-\frac{-\sqrt{2}-\sqrt{10}}{4}$$

\frac{3\times 4}{4} va \frac{-\sqrt{2}-\sqrt{10}}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{3\times 4-\left(-\sqrt{2}-\sqrt{10}\right)}{4}$$

3\times 4-\left(-\sqrt{2}-\sqrt{10}\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{12+\sqrt{2}+\sqrt{10}}{4}$$