Whakaoti i te 9^2=45^2+x^2

$${ 9 }^{ 2 } = { 45 }^{ 2 } + { x }^{ 2 }$$

Whakaoti mō x (complex solution)

$$x=-18\sqrt{6}i\approx -0-44.09081537i$$

$$x=18\sqrt{6}i\approx 44.09081537i$$

Ngā Upane mā te Kimi Pūtakerua

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

$$81=45^{2}+x^{2}$$

Tātaihia te 45 mā te pū o 2, kia riro ko 2025.

$$81=2025+x^{2}$$

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

$$2025+x^{2}=81$$

Tangohia te 2025 mai i ngā taha e rua.

$$x^{2}=81-2025$$

Tangohia te 2025 i te 81, ka -1944.

$$x^{2}=-1944$$

Kua oti te whārite te whakatau.

$$x=18\sqrt{6}i x=-18\sqrt{6}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$81=45^{2}+x^{2}$$

Tātaihia te 45 mā te pū o 2, kia riro ko 2025.

$$81=2025+x^{2}$$

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

$$2025+x^{2}=81$$

Tangohia te 81 mai i ngā taha e rua.

$$2025+x^{2}-81=0$$

Tangohia te 81 i te 2025, ka 1944.

$$1944+x^{2}=0$$

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.

$$x^{2}+1944=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me 1944 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1944}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 1944}}{2}$$

Whakareatia -4 ki te 1944.

$$x=\frac{0±\sqrt{-7776}}{2}$$

Tuhia te pūtakerua o te -7776.

$$x=\frac{0±36\sqrt{6}i}{2}$$

Nā, me whakaoti te whārite x=\frac{0±36\sqrt{6}i}{2} ina he tāpiri te ±.

$$x=18\sqrt{6}i$$

Nā, me whakaoti te whārite x=\frac{0±36\sqrt{6}i}{2} ina he tango te ±.

$$x=-18\sqrt{6}i$$

Kua oti te whārite te whakatau.

$$x=18\sqrt{6}i x=-18\sqrt{6}i$$