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

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

Luacháil

$$8-\sqrt{2}\approx 6.585786438$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(2\sqrt{2}-1\right)^{2} a leathnú.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Méadaigh 4 agus 2 chun 8 a fháil.

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

Suimigh 8 agus 1 chun 9 a fháil.

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

Suimigh -1 agus 9 chun 8 a fháil.

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

Comhcheangail \sqrt{2} agus -4\sqrt{2} chun -3\sqrt{2} a fháil.

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

Comhcheangail -3\sqrt{2} agus 2\sqrt{2} chun -\sqrt{2} a fháil.

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