Whakaoti i te 3^2=25^2+x^2

$${ 3 }^{ 2 } = { 25 }^{ 2 } + { x }^{ 2 }$$

Whakaoti mō x (complex solution)

$$x=-2\sqrt{154}i\approx -0-24.819347292i$$

$$x=2\sqrt{154}i\approx 24.819347292i$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$9=25^{2}+x^{2}$$

Tātaihia te 25 mā te pū o 2, kia riro ko 625.

$$9=625+x^{2}$$

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

$$625+x^{2}=9$$

Tangohia te 625 mai i ngā taha e rua.

$$x^{2}=9-625$$

Tangohia te 625 i te 9, ka -616.

$$x^{2}=-616$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{154}i x=-2\sqrt{154}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$9=25^{2}+x^{2}$$

Tātaihia te 25 mā te pū o 2, kia riro ko 625.

$$9=625+x^{2}$$

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

$$625+x^{2}=9$$

Tangohia te 9 mai i ngā taha e rua.

$$625+x^{2}-9=0$$

Tangohia te 9 i te 625, ka 616.

$$616+x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$x^{2}+616=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me 616 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 616}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 616}}{2}$$

Whakareatia -4 ki te 616.

$$x=\frac{0±\sqrt{-2464}}{2}$$

Tuhia te pūtakerua o te -2464.

$$x=\frac{0±4\sqrt{154}i}{2}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{154}i}{2} ina he tāpiri te ±.

$$x=2\sqrt{154}i$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{154}i}{2} ina he tango te ±.

$$x=-2\sqrt{154}i$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{154}i x=-2\sqrt{154}i$$