Whakaoti i te (7+3sqrt{2})^2-(5-2sqrt{5})^2

$$( 7 + 3 \sqrt { 2 } ) ^ { 2 } - ( 5 - 2 \sqrt { 5 } ) ^ { 2 }$$

Aromātai

$$20\sqrt{5}+42\sqrt{2}+22\approx 126.11832917$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(7+3\sqrt{2}\right)^{2}.

$$49+42\sqrt{2}+9\left(\sqrt{2}\right)^{2}-\left(5-2\sqrt{5}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$49+42\sqrt{2}+9\times 2-\left(5-2\sqrt{5}\right)^{2}$$

Whakareatia te 9 ki te 2, ka 18.

$$49+42\sqrt{2}+18-\left(5-2\sqrt{5}\right)^{2}$$

Tāpirihia te 49 ki te 18, ka 67.

$$67+42\sqrt{2}-\left(5-2\sqrt{5}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(5-2\sqrt{5}\right)^{2}.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\left(\sqrt{5}\right)^{2}\right)$$

Ko te pūrua o \sqrt{5} ko 5.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\times 5\right)$$

Whakareatia te 4 ki te 5, ka 20.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+20\right)$$

Tāpirihia te 25 ki te 20, ka 45.

$$67+42\sqrt{2}-\left(45-20\sqrt{5}\right)$$

Hei kimi i te tauaro o 45-20\sqrt{5}, kimihia te tauaro o ia taurangi.

$$67+42\sqrt{2}-45+20\sqrt{5}$$

Tangohia te 45 i te 67, ka 22.

$$22+42\sqrt{2}+20\sqrt{5}$$

Whakaroha

$$20 \sqrt{5} + 42 \sqrt{2} + 22 = 126.11832917$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(7+3\sqrt{2}\right)^{2}.

$$49+42\sqrt{2}+9\left(\sqrt{2}\right)^{2}-\left(5-2\sqrt{5}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$49+42\sqrt{2}+9\times 2-\left(5-2\sqrt{5}\right)^{2}$$

Whakareatia te 9 ki te 2, ka 18.

$$49+42\sqrt{2}+18-\left(5-2\sqrt{5}\right)^{2}$$

Tāpirihia te 49 ki te 18, ka 67.

$$67+42\sqrt{2}-\left(5-2\sqrt{5}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(5-2\sqrt{5}\right)^{2}.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\left(\sqrt{5}\right)^{2}\right)$$

Ko te pūrua o \sqrt{5} ko 5.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\times 5\right)$$

Whakareatia te 4 ki te 5, ka 20.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+20\right)$$

Tāpirihia te 25 ki te 20, ka 45.

$$67+42\sqrt{2}-\left(45-20\sqrt{5}\right)$$

Hei kimi i te tauaro o 45-20\sqrt{5}, kimihia te tauaro o ia taurangi.

$$67+42\sqrt{2}-45+20\sqrt{5}$$

Tangohia te 45 i te 67, ka 22.

$$22+42\sqrt{2}+20\sqrt{5}$$