Whakaoti i te (3+sqrt{2})^2-4(2-sqrt{2})

$$( 3 + \sqrt { 2 } ) ^ { 2 } - 4 ( 2 - \sqrt { 2 } )$$

Aromātai

$$10\sqrt{2}+3\approx 17.142135624$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(3+\sqrt{2}\right)^{2}.

$$9+6\sqrt{2}+\left(\sqrt{2}\right)^{2}-4\left(2-\sqrt{2}\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$9+6\sqrt{2}+2-4\left(2-\sqrt{2}\right)$$

Tāpirihia te 9 ki te 2, ka 11.

$$11+6\sqrt{2}-4\left(2-\sqrt{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -4 ki te 2-\sqrt{2}.

$$11+6\sqrt{2}-8+4\sqrt{2}$$

Tangohia te 8 i te 11, ka 3.

$$3+6\sqrt{2}+4\sqrt{2}$$

Pahekotia te 6\sqrt{2} me 4\sqrt{2}, ka 10\sqrt{2}.

$$3+10\sqrt{2}$$