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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(2\sqrt{2}-1\right)^{2}.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Immultiplika 4 u 2 biex tikseb 8.

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

Żid 8 u 1 biex tikseb 9.

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

Żid -1 u 9 biex tikseb 8.

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

Ikkombina \sqrt{2} u -4\sqrt{2} biex tikseb -3\sqrt{2}.

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

Ikkombina -3\sqrt{2} u 2\sqrt{2} biex tikseb -\sqrt{2}.

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