frac{sqrt{2}}{2sqrt{2}-1} eching

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

Baholash

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

Yechim qadamlari

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

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

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

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

\left(2\sqrt{2}\right)^{2} ni kengaytirish.

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

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

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

\sqrt{2} kvadrati – 2.

$$\frac{\sqrt{2}\left(2\sqrt{2}+1\right)}{4\times 2-1^{2}}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$\frac{\sqrt{2}\left(2\sqrt{2}+1\right)}{8-1^{2}}$$

2 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$\frac{\sqrt{2}\left(2\sqrt{2}+1\right)}{8-1}$$

7 olish uchun 8 dan 1 ni ayirish.

$$\frac{\sqrt{2}\left(2\sqrt{2}+1\right)}{7}$$

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

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

\sqrt{2} kvadrati – 2.

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

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

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