Whakaoti i te A/2n^{2}=11^2-107^2+96^2+59^2

$$\frac { A } { 2 } n ^ { 2 } = 11 ^ { 2 } - 107 ^ { 2 } + 96 ^ { 2 } + 59 ^ { 2 }$$

Whakaoti mō A

$$A=\frac{2738}{n^{2}}$$

$$n\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 2.

$$An^{2}=2\left(11^{2}-107^{2}\right)+2\times 96^{2}+2\times 59^{2}$$

Tātaihia te 11 mā te pū o 2, kia riro ko 121.

$$An^{2}=2\left(121-107^{2}\right)+2\times 96^{2}+2\times 59^{2}$$

Tātaihia te 107 mā te pū o 2, kia riro ko 11449.

$$An^{2}=2\left(121-11449\right)+2\times 96^{2}+2\times 59^{2}$$

Tangohia te 11449 i te 121, ka -11328.

$$An^{2}=2\left(-11328\right)+2\times 96^{2}+2\times 59^{2}$$

Whakareatia te 2 ki te -11328, ka -22656.

$$An^{2}=-22656+2\times 96^{2}+2\times 59^{2}$$

Tātaihia te 96 mā te pū o 2, kia riro ko 9216.

$$An^{2}=-22656+2\times 9216+2\times 59^{2}$$

Whakareatia te 2 ki te 9216, ka 18432.

$$An^{2}=-22656+18432+2\times 59^{2}$$

Tāpirihia te -22656 ki te 18432, ka -4224.

$$An^{2}=-4224+2\times 59^{2}$$

Tātaihia te 59 mā te pū o 2, kia riro ko 3481.

$$An^{2}=-4224+2\times 3481$$

Whakareatia te 2 ki te 3481, ka 6962.

$$An^{2}=-4224+6962$$

Tāpirihia te -4224 ki te 6962, ka 2738.

$$An^{2}=2738$$

He hanga arowhānui tō te whārite.

$$n^{2}A=2738$$

Whakawehea ngā taha e rua ki te n^{2}.

$$\frac{n^{2}A}{n^{2}}=\frac{2738}{n^{2}}$$

Mā te whakawehe ki te n^{2} ka wetekia te whakareanga ki te n^{2}.

$$A=\frac{2738}{n^{2}}$$

Whakaoti mō n (complex solution)

$$n=-37\sqrt{2}A^{-\frac{1}{2}}$$

$$n=37\sqrt{2}A^{-\frac{1}{2}}\text{, }A\neq 0$$

Whakaoti mō n

$$n=37\sqrt{\frac{2}{A}}$$

$$n=-37\sqrt{\frac{2}{A}}\text{, }A>0$$