Whakaoti i te {left(16*x/10right)}^2+x^2=4318^2

$${ \left( \frac{ 16 \times x }{ 10 } \right) }^{ 2 } + { x }^{ 2 } = { 4318 }^{ 2 }$$

Whakaoti mō x

$$x = \frac{21590 \sqrt{89}}{89} \approx 2288.535422934$$

$$x = -\frac{21590 \sqrt{89}}{89} \approx -2288.535422934$$

Ngā Upane mā te Kimi Pūtakerua

Whakawehea te 16x ki te 10, kia riro ko \frac{8}{5}x.

$$\left(\frac{8}{5}x\right)^{2}+x^{2}=4318^{2}$$

Whakarohaina te \left(\frac{8}{5}x\right)^{2}.

$$\left(\frac{8}{5}\right)^{2}x^{2}+x^{2}=4318^{2}$$

Tātaihia te \frac{8}{5} mā te pū o 2, kia riro ko \frac{64}{25}.

$$\frac{64}{25}x^{2}+x^{2}=4318^{2}$$

Pahekotia te \frac{64}{25}x^{2} me x^{2}, ka \frac{89}{25}x^{2}.

$$\frac{89}{25}x^{2}=4318^{2}$$

Tātaihia te 4318 mā te pū o 2, kia riro ko 18645124.

$$\frac{89}{25}x^{2}=18645124$$

Me whakarea ngā taha e rua ki te \frac{25}{89}, te tau utu o \frac{89}{25}.

$$x^{2}=18645124\times \frac{25}{89}$$

Whakareatia te 18645124 ki te \frac{25}{89}, ka \frac{466128100}{89}.

$$x^{2}=\frac{466128100}{89}$$

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

$$x=\frac{21590\sqrt{89}}{89} x=-\frac{21590\sqrt{89}}{89}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea te 16x ki te 10, kia riro ko \frac{8}{5}x.

$$\left(\frac{8}{5}x\right)^{2}+x^{2}=4318^{2}$$

Whakarohaina te \left(\frac{8}{5}x\right)^{2}.

$$\left(\frac{8}{5}\right)^{2}x^{2}+x^{2}=4318^{2}$$

Tātaihia te \frac{8}{5} mā te pū o 2, kia riro ko \frac{64}{25}.

$$\frac{64}{25}x^{2}+x^{2}=4318^{2}$$

Pahekotia te \frac{64}{25}x^{2} me x^{2}, ka \frac{89}{25}x^{2}.

$$\frac{89}{25}x^{2}=4318^{2}$$

Tātaihia te 4318 mā te pū o 2, kia riro ko 18645124.

$$\frac{89}{25}x^{2}=18645124$$

Tangohia te 18645124 mai i ngā taha e rua.

$$\frac{89}{25}x^{2}-18645124=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{89}{25} mō a, 0 mō b, me -18645124 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{89}{25}\left(-18645124\right)}}{2\times \frac{89}{25}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{89}{25}\left(-18645124\right)}}{2\times \frac{89}{25}}$$

Whakareatia -4 ki te \frac{89}{25}.

$$x=\frac{0±\sqrt{-\frac{356}{25}\left(-18645124\right)}}{2\times \frac{89}{25}}$$

Whakareatia -\frac{356}{25} ki te -18645124.

$$x=\frac{0±\sqrt{\frac{6637664144}{25}}}{2\times \frac{89}{25}}$$

Tuhia te pūtakerua o te \frac{6637664144}{25}.

$$x=\frac{0±\frac{8636\sqrt{89}}{5}}{2\times \frac{89}{25}}$$

Whakareatia 2 ki te \frac{89}{25}.

$$x=\frac{0±\frac{8636\sqrt{89}}{5}}{\frac{178}{25}}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{8636\sqrt{89}}{5}}{\frac{178}{25}} ina he tāpiri te ±.

$$x=\frac{21590\sqrt{89}}{89}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{8636\sqrt{89}}{5}}{\frac{178}{25}} ina he tango te ±.

$$x=-\frac{21590\sqrt{89}}{89}$$

Kua oti te whārite te whakatau.

$$x=\frac{21590\sqrt{89}}{89} x=-\frac{21590\sqrt{89}}{89}$$