Whakaoti i te 8^2+10^2=C^2

$$8 ^ { 2 } + 10 ^ { 2 } = C ^ { 2 }$$

Whakaoti mō C

$$C=2\sqrt{41}\approx 12.806248475$$

$$C=-2\sqrt{41}\approx -12.806248475$$

Ngā Upane mā te Kimi Pūtakerua

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

$$64+10^{2}=C^{2}$$

Tātaihia te 10 mā te pū o 2, kia riro ko 100.

$$64+100=C^{2}$$

Tāpirihia te 64 ki te 100, ka 164.

$$164=C^{2}$$

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

$$C^{2}=164$$

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

$$C=2\sqrt{41} C=-2\sqrt{41}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$64+10^{2}=C^{2}$$

Tātaihia te 10 mā te pū o 2, kia riro ko 100.

$$64+100=C^{2}$$

Tāpirihia te 64 ki te 100, ka 164.

$$164=C^{2}$$

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

$$C^{2}=164$$

Tangohia te 164 mai i ngā taha e rua.

$$C^{2}-164=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -164 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$C=\frac{0±\sqrt{0^{2}-4\left(-164\right)}}{2}$$

Pūrua 0.

$$C=\frac{0±\sqrt{-4\left(-164\right)}}{2}$$

Whakareatia -4 ki te -164.

$$C=\frac{0±\sqrt{656}}{2}$$

Tuhia te pūtakerua o te 656.

$$C=\frac{0±4\sqrt{41}}{2}$$

Nā, me whakaoti te whārite C=\frac{0±4\sqrt{41}}{2} ina he tāpiri te ±.

$$C=2\sqrt{41}$$

Nā, me whakaoti te whārite C=\frac{0±4\sqrt{41}}{2} ina he tango te ±.

$$C=-2\sqrt{41}$$

Kua oti te whārite te whakatau.

$$C=2\sqrt{41} C=-2\sqrt{41}$$