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

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

Izrēķināt

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

Atrisinājuma darbības

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(2\sqrt{2}-1\right)^{2}.

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

Skaitļa \sqrt{2} kvadrāts ir 2.

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

Reiziniet 4 un 2, lai iegūtu 8.

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

Saskaitiet 8 un 1, lai iegūtu 9.

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

Saskaitiet -1 un 9, lai iegūtu 8.

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

Savelciet \sqrt{2} un -4\sqrt{2}, lai iegūtu -3\sqrt{2}.

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

Savelciet -3\sqrt{2} un 2\sqrt{2}, lai iegūtu -\sqrt{2}.

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