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

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

Arvuta

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

Lahenduse etapid

Kasutage kaksliikme \left(2\sqrt{2}-1\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{2} ruut on 2.

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

Korrutage 4 ja 2, et leida 8.

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

Liitke 8 ja 1, et leida 9.

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

Liitke -1 ja 9, et leida 8.

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

Kombineerige \sqrt{2} ja -4\sqrt{2}, et leida -3\sqrt{2}.

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

Kombineerige -3\sqrt{2} ja 2\sqrt{2}, et leida -\sqrt{2}.

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