Whakaoti i te c^2=13^2+84^2

$$c ^ { 2 } = 13 ^ { 2 } + 84 ^ { 2 }$$

Whakaoti mō c

$$c=-85$$

$$c=85$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tātaihia te 13 mā te pū o 2, kia riro ko 169.

$$c^{2}=169+84^{2}$$

Tātaihia te 84 mā te pū o 2, kia riro ko 7056.

$$c^{2}=169+7056$$

Tāpirihia te 169 ki te 7056, ka 7225.

$$c^{2}=7225$$

Tangohia te 7225 mai i ngā taha e rua.

$$c^{2}-7225=0$$

Whakaarohia te c^{2}-7225. Tuhia anō te c^{2}-7225 hei c^{2}-85^{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).

$$\left(c-85\right)\left(c+85\right)=0$$

Hei kimi otinga whārite, me whakaoti te c-85=0 me te c+85=0.

$$c=85 c=-85$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 13 mā te pū o 2, kia riro ko 169.

$$c^{2}=169+84^{2}$$

Tātaihia te 84 mā te pū o 2, kia riro ko 7056.

$$c^{2}=169+7056$$

Tāpirihia te 169 ki te 7056, ka 7225.

$$c^{2}=7225$$

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

$$c=85 c=-85$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 13 mā te pū o 2, kia riro ko 169.

$$c^{2}=169+84^{2}$$

Tātaihia te 84 mā te pū o 2, kia riro ko 7056.

$$c^{2}=169+7056$$

Tāpirihia te 169 ki te 7056, ka 7225.

$$c^{2}=7225$$

Tangohia te 7225 mai i ngā taha e rua.

$$c^{2}-7225=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -7225 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-7225\right)}}{2}$$

Pūrua 0.

$$c=\frac{0±\sqrt{-4\left(-7225\right)}}{2}$$

Whakareatia -4 ki te -7225.

$$c=\frac{0±\sqrt{28900}}{2}$$

Tuhia te pūtakerua o te 28900.

$$c=\frac{0±170}{2}$$

Nā, me whakaoti te whārite c=\frac{0±170}{2} ina he tāpiri te ±. Whakawehe 170 ki te 2.

$$c=85$$

Nā, me whakaoti te whārite c=\frac{0±170}{2} ina he tango te ±. Whakawehe -170 ki te 2.

$$c=-85$$

Kua oti te whārite te whakatau.

$$c=85 c=-85$$