Whakaoti i te 25^2/75^2+x^2/45^2=1

$$\frac{ { 25 }^{ 2 } }{ { 75 }^{ 2 } } + \frac{ { x }^{ 2 } }{ { 45 }^{ 2 } } = 1$$

Whakaoti mō x

$$x=30\sqrt{2}\approx 42.426406871$$

$$x=-30\sqrt{2}\approx -42.426406871$$

Ngā Upane mā te Kimi Pūtakerua

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

$$\frac{625}{75^{2}}+\frac{x^{2}}{45^{2}}=1$$

Tātaihia te 75 mā te pū o 2, kia riro ko 5625.

$$\frac{625}{5625}+\frac{x^{2}}{45^{2}}=1$$

Whakahekea te hautanga \frac{625}{5625} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 625.

$$\frac{1}{9}+\frac{x^{2}}{45^{2}}=1$$

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

$$\frac{1}{9}+\frac{x^{2}}{2025}=1$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 9 me 2025 ko 2025. Whakareatia \frac{1}{9} ki te \frac{225}{225}.

$$\frac{225}{2025}+\frac{x^{2}}{2025}=1$$

Tā te mea he rite te tauraro o \frac{225}{2025} me \frac{x^{2}}{2025}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{225+x^{2}}{2025}=1$$

Whakawehea ia wā o 225+x^{2} ki te 2025, kia riro ko \frac{1}{9}+\frac{1}{2025}x^{2}.

$$\frac{1}{9}+\frac{1}{2025}x^{2}=1$$

Tangohia te \frac{1}{9} mai i ngā taha e rua.

$$\frac{1}{2025}x^{2}=1-\frac{1}{9}$$

Tangohia te \frac{1}{9} i te 1, ka \frac{8}{9}.

$$\frac{1}{2025}x^{2}=\frac{8}{9}$$

Me whakarea ngā taha e rua ki te 2025, te tau utu o \frac{1}{2025}.

$$x^{2}=\frac{8}{9}\times 2025$$

Whakareatia te \frac{8}{9} ki te 2025, ka 1800.

$$x^{2}=1800$$

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

$$x=30\sqrt{2} x=-30\sqrt{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$\frac{625}{75^{2}}+\frac{x^{2}}{45^{2}}=1$$

Tātaihia te 75 mā te pū o 2, kia riro ko 5625.

$$\frac{625}{5625}+\frac{x^{2}}{45^{2}}=1$$

Whakahekea te hautanga \frac{625}{5625} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 625.

$$\frac{1}{9}+\frac{x^{2}}{45^{2}}=1$$

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

$$\frac{1}{9}+\frac{x^{2}}{2025}=1$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 9 me 2025 ko 2025. Whakareatia \frac{1}{9} ki te \frac{225}{225}.

$$\frac{225}{2025}+\frac{x^{2}}{2025}=1$$

Tā te mea he rite te tauraro o \frac{225}{2025} me \frac{x^{2}}{2025}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{225+x^{2}}{2025}=1$$

Whakawehea ia wā o 225+x^{2} ki te 2025, kia riro ko \frac{1}{9}+\frac{1}{2025}x^{2}.

$$\frac{1}{9}+\frac{1}{2025}x^{2}=1$$

Tangohia te 1 mai i ngā taha e rua.

$$\frac{1}{9}+\frac{1}{2025}x^{2}-1=0$$

Tangohia te 1 i te \frac{1}{9}, ka -\frac{8}{9}.

$$-\frac{8}{9}+\frac{1}{2025}x^{2}=0$$

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.

$$\frac{1}{2025}x^{2}-\frac{8}{9}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1}{2025} mō a, 0 mō b, me -\frac{8}{9} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2025}\left(-\frac{8}{9}\right)}}{2\times \frac{1}{2025}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2025}\left(-\frac{8}{9}\right)}}{2\times \frac{1}{2025}}$$

Whakareatia -4 ki te \frac{1}{2025}.

$$x=\frac{0±\sqrt{-\frac{4}{2025}\left(-\frac{8}{9}\right)}}{2\times \frac{1}{2025}}$$

Whakareatia -\frac{4}{2025} ki te -\frac{8}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{0±\sqrt{\frac{32}{18225}}}{2\times \frac{1}{2025}}$$

Tuhia te pūtakerua o te \frac{32}{18225}.

$$x=\frac{0±\frac{4\sqrt{2}}{135}}{2\times \frac{1}{2025}}$$

Whakareatia 2 ki te \frac{1}{2025}.

$$x=\frac{0±\frac{4\sqrt{2}}{135}}{\frac{2}{2025}}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{4\sqrt{2}}{135}}{\frac{2}{2025}} ina he tāpiri te ±.

$$x=30\sqrt{2}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{4\sqrt{2}}{135}}{\frac{2}{2025}} ina he tango te ±.

$$x=-30\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=30\sqrt{2} x=-30\sqrt{2}$$