Whakaoti i te 3*(2+sqrt{7})^2-12*(2+sqrt{7})+13

$$3 \times ( 2 + \sqrt { 7 } ) ^ { 2 } - 12 \times ( 2 + \sqrt { 7 } ) + 13$$

Aromātai

$$22$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2+\sqrt{7}\right)^{2}.

$$3\left(4+4\sqrt{7}+\left(\sqrt{7}\right)^{2}\right)-12\left(2+\sqrt{7}\right)+13$$

Ko te pūrua o \sqrt{7} ko 7.

$$3\left(4+4\sqrt{7}+7\right)-12\left(2+\sqrt{7}\right)+13$$

Tāpirihia te 4 ki te 7, ka 11.

$$3\left(11+4\sqrt{7}\right)-12\left(2+\sqrt{7}\right)+13$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 11+4\sqrt{7}.

$$33+12\sqrt{7}-12\left(2+\sqrt{7}\right)+13$$

Whakamahia te āhuatanga tohatoha hei whakarea te -12 ki te 2+\sqrt{7}.

$$33+12\sqrt{7}-24-12\sqrt{7}+13$$

Tangohia te 24 i te 33, ka 9.

$$9+12\sqrt{7}-12\sqrt{7}+13$$

Pahekotia te 12\sqrt{7} me -12\sqrt{7}, ka 0.

$$9+13$$

Tāpirihia te 9 ki te 13, ka 22.

$$22$$

Tauwehe

$$2\times 11$$