1/2-sqrt{2}+1/sqrt{2-1}):1/2 eching

$$\frac { 1 } { 2 - \sqrt { 2 } } + \frac { 1 } { \sqrt { 2 } - 1 } ) : \frac { 1 } { 2 }$$

Baholash

$$\frac{3\sqrt{2}}{2}+2\approx 4,121320344$$

Qisqa yechim qadamlari

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

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

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

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

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

$$\frac{2+\sqrt{2}}{4-2}+\frac{1}{\sqrt{2}-1}$$

2 olish uchun 4 dan 2 ni ayirish.

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

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

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

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

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

\sqrt{2} kvadratini chiqarish. 1 kvadratini chiqarish.

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

1 olish uchun 2 dan 1 ni ayirish.

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

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \sqrt{2}+1 ni \frac{2}{2} marotabaga ko'paytirish.

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

\frac{2+\sqrt{2}}{2} va \frac{2\left(\sqrt{2}+1\right)}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

2+\sqrt{2}+2\left(\sqrt{2}+1\right) ichidagi ko‘paytirishlarni bajaring.

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

2+\sqrt{2}+2\sqrt{2}+2 hisob-kitobini qiling.

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