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

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

Whakaoti mō n

$$n=-37$$

$$n=37$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$1n^{2}=11^{2}-107^{2}+96^{2}+59^{2}$$

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

$$1n^{2}=121-107^{2}+96^{2}+59^{2}$$

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

$$1n^{2}=121-11449+96^{2}+59^{2}$$

Tangohia te 11449 i te 121, ka -11328.

$$1n^{2}=-11328+96^{2}+59^{2}$$

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

$$1n^{2}=-11328+9216+59^{2}$$

Tāpirihia te -11328 ki te 9216, ka -2112.

$$1n^{2}=-2112+59^{2}$$

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

$$1n^{2}=-2112+3481$$

Tāpirihia te -2112 ki te 3481, ka 1369.

$$1n^{2}=1369$$

Tangohia te 1369 mai i ngā taha e rua.

$$1n^{2}-1369=0$$

Whakaraupapatia anō ngā kīanga tau.

$$n^{2}-1369=0$$

Whakaarohia te n^{2}-1369. Tuhia anō te n^{2}-1369 hei n^{2}-37^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-37\right)\left(n+37\right)=0$$

Hei kimi otinga whārite, me whakaoti te n-37=0 me te n+37=0.

$$n=37 n=-37$$

Ngā Upane mā te Kimi Pūtakerua

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$1n^{2}=11^{2}-107^{2}+96^{2}+59^{2}$$

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

$$1n^{2}=121-107^{2}+96^{2}+59^{2}$$

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

$$1n^{2}=121-11449+96^{2}+59^{2}$$

Tangohia te 11449 i te 121, ka -11328.

$$1n^{2}=-11328+96^{2}+59^{2}$$

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

$$1n^{2}=-11328+9216+59^{2}$$

Tāpirihia te -11328 ki te 9216, ka -2112.

$$1n^{2}=-2112+59^{2}$$

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

$$1n^{2}=-2112+3481$$

Tāpirihia te -2112 ki te 3481, ka 1369.

$$1n^{2}=1369$$

Whakawehea ngā taha e rua ki te 1.

$$n^{2}=1369$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$n=37 n=-37$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$1n^{2}=11^{2}-107^{2}+96^{2}+59^{2}$$

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

$$1n^{2}=121-107^{2}+96^{2}+59^{2}$$

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

$$1n^{2}=121-11449+96^{2}+59^{2}$$

Tangohia te 11449 i te 121, ka -11328.

$$1n^{2}=-11328+96^{2}+59^{2}$$

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

$$1n^{2}=-11328+9216+59^{2}$$

Tāpirihia te -11328 ki te 9216, ka -2112.

$$1n^{2}=-2112+59^{2}$$

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

$$1n^{2}=-2112+3481$$

Tāpirihia te -2112 ki te 3481, ka 1369.

$$1n^{2}=1369$$

Tangohia te 1369 mai i ngā taha e rua.

$$1n^{2}-1369=0$$

Whakaraupapatia anō ngā kīanga tau.

$$n^{2}-1369=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -1369 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-1369\right)}}{2}$$

Pūrua 0.

$$n=\frac{0±\sqrt{-4\left(-1369\right)}}{2}$$

Whakareatia -4 ki te -1369.

$$n=\frac{0±\sqrt{5476}}{2}$$

Tuhia te pūtakerua o te 5476.

$$n=\frac{0±74}{2}$$

Nā, me whakaoti te whārite n=\frac{0±74}{2} ina he tāpiri te ±. Whakawehe 74 ki te 2.

$$n=37$$

Nā, me whakaoti te whārite n=\frac{0±74}{2} ina he tango te ±. Whakawehe -74 ki te 2.

$$n=-37$$

Kua oti te whārite te whakatau.

$$n=37 n=-37$$