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

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

Baholash

$$\frac{\sqrt{2}+\sqrt{10}-3\sqrt{5}-3}{4}\approx -1,282928177$$

Yechim qadamlari

\frac{3-\sqrt{2}}{1-\sqrt{5}} maxrajini 1+\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

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}.

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

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

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

-4 olish uchun 1 dan 5 ni ayirish.

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

3-\sqrt{2} ifodaning har bir elementini 1+\sqrt{5} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

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

$$\frac{3+3\sqrt{5}-\sqrt{2}-\sqrt{10}}{-4}$$

Surat va maxrajini -1 ga ko‘paytiring.

$$\frac{-3-3\sqrt{5}+\sqrt{2}+\sqrt{10}}{4}$$