((sqrt{2}-1+{left(2sqrt{2}-1right)}^2+2sqrt{2}) eching

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

Baholash

$$8-\sqrt{2}\approx 6,585786438$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2\sqrt{2}-1\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{2} kvadrati – 2.

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

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

$$\sqrt{2}-1+8-4\sqrt{2}+1+2\sqrt{2}$$

9 olish uchun 8 va 1'ni qo'shing.

$$\sqrt{2}-1+9-4\sqrt{2}+2\sqrt{2}$$

8 olish uchun -1 va 9'ni qo'shing.

$$\sqrt{2}+8-4\sqrt{2}+2\sqrt{2}$$

-3\sqrt{2} ni olish uchun \sqrt{2} va -4\sqrt{2} ni birlashtirish.

$$-3\sqrt{2}+8+2\sqrt{2}$$

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

$$-\sqrt{2}+8$$