Whakaoti i te 105^2=(9x)^2+(32x)^2

$$105 ^ { 2 } = ( 9 x ) ^ { 2 } + ( 32 x ) ^ { 2 }$$

Whakaoti mō x

$$x = \frac{21 \sqrt{1105}}{221} \approx 3.158698397$$

$$x = -\frac{21 \sqrt{1105}}{221} \approx -3.158698397$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 105 mā te pū o 2, kia riro ko 11025.

$$11025=\left(9x\right)^{2}+\left(32x\right)^{2}$$

Whakarohaina te \left(9x\right)^{2}.

$$11025=9^{2}x^{2}+\left(32x\right)^{2}$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$11025=81x^{2}+\left(32x\right)^{2}$$

Whakarohaina te \left(32x\right)^{2}.

$$11025=81x^{2}+32^{2}x^{2}$$

Tātaihia te 32 mā te pū o 2, kia riro ko 1024.

$$11025=81x^{2}+1024x^{2}$$

Pahekotia te 81x^{2} me 1024x^{2}, ka 1105x^{2}.

$$11025=1105x^{2}$$

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

$$1105x^{2}=11025$$

Whakawehea ngā taha e rua ki te 1105.

$$x^{2}=\frac{11025}{1105}$$

Whakahekea te hautanga \frac{11025}{1105} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x^{2}=\frac{2205}{221}$$

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

$$x=\frac{21\sqrt{1105}}{221} x=-\frac{21\sqrt{1105}}{221}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 105 mā te pū o 2, kia riro ko 11025.

$$11025=\left(9x\right)^{2}+\left(32x\right)^{2}$$

Whakarohaina te \left(9x\right)^{2}.

$$11025=9^{2}x^{2}+\left(32x\right)^{2}$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$11025=81x^{2}+\left(32x\right)^{2}$$

Whakarohaina te \left(32x\right)^{2}.

$$11025=81x^{2}+32^{2}x^{2}$$

Tātaihia te 32 mā te pū o 2, kia riro ko 1024.

$$11025=81x^{2}+1024x^{2}$$

Pahekotia te 81x^{2} me 1024x^{2}, ka 1105x^{2}.

$$11025=1105x^{2}$$

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

$$1105x^{2}=11025$$

Tangohia te 11025 mai i ngā taha e rua.

$$1105x^{2}-11025=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1105 mō a, 0 mō b, me -11025 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1105\left(-11025\right)}}{2\times 1105}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 1105\left(-11025\right)}}{2\times 1105}$$

Whakareatia -4 ki te 1105.

$$x=\frac{0±\sqrt{-4420\left(-11025\right)}}{2\times 1105}$$

Whakareatia -4420 ki te -11025.

$$x=\frac{0±\sqrt{48730500}}{2\times 1105}$$

Tuhia te pūtakerua o te 48730500.

$$x=\frac{0±210\sqrt{1105}}{2\times 1105}$$

Whakareatia 2 ki te 1105.

$$x=\frac{0±210\sqrt{1105}}{2210}$$

Nā, me whakaoti te whārite x=\frac{0±210\sqrt{1105}}{2210} ina he tāpiri te ±.

$$x=\frac{21\sqrt{1105}}{221}$$

Nā, me whakaoti te whārite x=\frac{0±210\sqrt{1105}}{2210} ina he tango te ±.

$$x=-\frac{21\sqrt{1105}}{221}$$

Kua oti te whārite te whakatau.

$$x=\frac{21\sqrt{1105}}{221} x=-\frac{21\sqrt{1105}}{221}$$