frac{2+sqrt{2}}{3+sqrt{2}} eching

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

Baholash

$$\frac{\sqrt{2}+4}{7}\approx 0,77345908$$

Yechim qadamlari

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

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

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

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

3 kvadratini chiqarish. \sqrt{2} kvadratini chiqarish.

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

7 olish uchun 9 dan 2 ni ayirish.

$$\frac{\left(2+\sqrt{2}\right)\left(3-\sqrt{2}\right)}{7}$$

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

$$\frac{6-2\sqrt{2}+3\sqrt{2}-\left(\sqrt{2}\right)^{2}}{7}$$

\sqrt{2} ni olish uchun -2\sqrt{2} va 3\sqrt{2} ni birlashtirish.

$$\frac{6+\sqrt{2}-\left(\sqrt{2}\right)^{2}}{7}$$

\sqrt{2} kvadrati – 2.

$$\frac{6+\sqrt{2}-2}{7}$$

4 olish uchun 6 dan 2 ni ayirish.

$$\frac{4+\sqrt{2}}{7}$$

Omil

$$\frac{\sqrt{2} + 4}{7} = 0,7734590803390136$$