Whakaoti i te 6^2+8^2=c^2

$$6 ^ { 2 } + 8 ^ { 2 } = c ^ { 2 }$$

Whakaoti mō c

$$c=10$$

$$c=-10$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$36+8^{2}=c^{2}$$

Tātaihia te 8 mā te pū o 2, kia riro ko 64.

$$36+64=c^{2}$$

Tāpirihia te 36 ki te 64, ka 100.

$$100=c^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$c^{2}=100$$

Tangohia te 100 mai i ngā taha e rua.

$$c^{2}-100=0$$

Whakaarohia te c^{2}-100. Tuhia anō te c^{2}-100 hei c^{2}-10^{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).

$$\left(c-10\right)\left(c+10\right)=0$$

Hei kimi otinga whārite, me whakaoti te c-10=0 me te c+10=0.

$$c=10 c=-10$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$36+8^{2}=c^{2}$$

Tātaihia te 8 mā te pū o 2, kia riro ko 64.

$$36+64=c^{2}$$

Tāpirihia te 36 ki te 64, ka 100.

$$100=c^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$c^{2}=100$$

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

$$c=10 c=-10$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$36+8^{2}=c^{2}$$

Tātaihia te 8 mā te pū o 2, kia riro ko 64.

$$36+64=c^{2}$$

Tāpirihia te 36 ki te 64, ka 100.

$$100=c^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$c^{2}=100$$

Tangohia te 100 mai i ngā taha e rua.

$$c^{2}-100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-100\right)}}{2}$$

Pūrua 0.

$$c=\frac{0±\sqrt{-4\left(-100\right)}}{2}$$

Whakareatia -4 ki te -100.

$$c=\frac{0±\sqrt{400}}{2}$$

Tuhia te pūtakerua o te 400.

$$c=\frac{0±20}{2}$$

Nā, me whakaoti te whārite c=\frac{0±20}{2} ina he tāpiri te ±. Whakawehe 20 ki te 2.

$$c=10$$

Nā, me whakaoti te whārite c=\frac{0±20}{2} ina he tango te ±. Whakawehe -20 ki te 2.

$$c=-10$$

Kua oti te whārite te whakatau.

$$c=10 c=-10$$