Whakaoti i te ((sqrt{2}-1+{left(2sqrt{2}-1right)}^2+2sqrt{2})

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

Aromātai

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

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2\sqrt{2}-1\right)^{2}.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Whakareatia te 4 ki te 2, ka 8.

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

Tāpirihia te 8 ki te 1, ka 9.

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

Tāpirihia te -1 ki te 9, ka 8.

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

Pahekotia te \sqrt{2} me -4\sqrt{2}, ka -3\sqrt{2}.

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

Pahekotia te -3\sqrt{2} me 2\sqrt{2}, ka -\sqrt{2}.

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