Whakaoti i te (sqrt{7}+3)^2-(sqrt{14}-sqrt{2})^2

$$( \sqrt { 7 } + 3 ) ^ { 2 } - ( \sqrt { 14 } - \sqrt { 2 } ) ^ { 2 }$$

Aromātai

$$10\sqrt{7}\approx 26.457513111$$

Ngā Upane Otinga

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

$$\left(\sqrt{7}\right)^{2}+6\sqrt{7}+9-\left(\sqrt{14}-\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{7} ko 7.

$$7+6\sqrt{7}+9-\left(\sqrt{14}-\sqrt{2}\right)^{2}$$

Tāpirihia te 7 ki te 9, ka 16.

$$16+6\sqrt{7}-\left(\sqrt{14}-\sqrt{2}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{14}-\sqrt{2}\right)^{2}.

$$16+6\sqrt{7}-\left(\left(\sqrt{14}\right)^{2}-2\sqrt{14}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Ko te pūrua o \sqrt{14} ko 14.

$$16+6\sqrt{7}-\left(14-2\sqrt{14}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Tauwehea te 14=2\times 7. Tuhia anō te pūtake rua o te hua \sqrt{2\times 7} hei hua o ngā pūtake rua \sqrt{2}\sqrt{7}.

$$16+6\sqrt{7}-\left(14-2\sqrt{2}\sqrt{7}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$16+6\sqrt{7}-\left(14-2\times 2\sqrt{7}+\left(\sqrt{2}\right)^{2}\right)$$

Whakareatia te -2 ki te 2, ka -4.

$$16+6\sqrt{7}-\left(14-4\sqrt{7}+\left(\sqrt{2}\right)^{2}\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$16+6\sqrt{7}-\left(14-4\sqrt{7}+2\right)$$

Tāpirihia te 14 ki te 2, ka 16.

$$16+6\sqrt{7}-\left(16-4\sqrt{7}\right)$$

Hei kimi i te tauaro o 16-4\sqrt{7}, kimihia te tauaro o ia taurangi.

$$16+6\sqrt{7}-16+4\sqrt{7}$$

Tangohia te 16 i te 16, ka 0.

$$6\sqrt{7}+4\sqrt{7}$$

Pahekotia te 6\sqrt{7} me 4\sqrt{7}, ka 10\sqrt{7}.

$$10\sqrt{7}$$

Whakaroha

$$10 \sqrt{7} = 26.457513111$$

Ngā Upane Otinga

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

$$\left(\sqrt{7}\right)^{2}+6\sqrt{7}+9-\left(\sqrt{14}-\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{7} ko 7.

$$7+6\sqrt{7}+9-\left(\sqrt{14}-\sqrt{2}\right)^{2}$$

Tāpirihia te 7 ki te 9, ka 16.

$$16+6\sqrt{7}-\left(\sqrt{14}-\sqrt{2}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{14}-\sqrt{2}\right)^{2}.

$$16+6\sqrt{7}-\left(\left(\sqrt{14}\right)^{2}-2\sqrt{14}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Ko te pūrua o \sqrt{14} ko 14.

$$16+6\sqrt{7}-\left(14-2\sqrt{14}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Tauwehea te 14=2\times 7. Tuhia anō te pūtake rua o te hua \sqrt{2\times 7} hei hua o ngā pūtake rua \sqrt{2}\sqrt{7}.

$$16+6\sqrt{7}-\left(14-2\sqrt{2}\sqrt{7}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$16+6\sqrt{7}-\left(14-2\times 2\sqrt{7}+\left(\sqrt{2}\right)^{2}\right)$$

Whakareatia te -2 ki te 2, ka -4.

$$16+6\sqrt{7}-\left(14-4\sqrt{7}+\left(\sqrt{2}\right)^{2}\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$16+6\sqrt{7}-\left(14-4\sqrt{7}+2\right)$$

Tāpirihia te 14 ki te 2, ka 16.

$$16+6\sqrt{7}-\left(16-4\sqrt{7}\right)$$

Hei kimi i te tauaro o 16-4\sqrt{7}, kimihia te tauaro o ia taurangi.

$$16+6\sqrt{7}-16+4\sqrt{7}$$

Tangohia te 16 i te 16, ka 0.

$$6\sqrt{7}+4\sqrt{7}$$

Pahekotia te 6\sqrt{7} me 4\sqrt{7}, ka 10\sqrt{7}.

$$10\sqrt{7}$$