Whakaoti i te 9-y^2/25-y^2/36=1

$$\frac { 9 - y ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 36 } = 1$$

Whakaoti mō y

$$y=-\frac{24\sqrt{61}i}{61}\approx -0-3.072885118i$$

$$y=\frac{24\sqrt{61}i}{61}\approx 3.072885118i$$

Ngā Upane mā te Kimi Pūtakerua

Me whakarea ngā taha e rua o te whārite ki te 900, arā, te tauraro pātahi he tino iti rawa te kitea o 25,36.

$$36\left(9-y^{2}\right)-25y^{2}=900$$

Whakamahia te āhuatanga tohatoha hei whakarea te 36 ki te 9-y^{2}.

$$324-36y^{2}-25y^{2}=900$$

Pahekotia te -36y^{2} me -25y^{2}, ka -61y^{2}.

$$324-61y^{2}=900$$

Tangohia te 324 mai i ngā taha e rua.

$$-61y^{2}=900-324$$

Tangohia te 324 i te 900, ka 576.

$$-61y^{2}=576$$

Whakawehea ngā taha e rua ki te -61.

$$y^{2}=-\frac{576}{61}$$

Kua oti te whārite te whakatau.

$$y=\frac{24\sqrt{61}i}{61} y=-\frac{24\sqrt{61}i}{61}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 900, arā, te tauraro pātahi he tino iti rawa te kitea o 25,36.

$$36\left(9-y^{2}\right)-25y^{2}=900$$

Whakamahia te āhuatanga tohatoha hei whakarea te 36 ki te 9-y^{2}.

$$324-36y^{2}-25y^{2}=900$$

Pahekotia te -36y^{2} me -25y^{2}, ka -61y^{2}.

$$324-61y^{2}=900$$

Tangohia te 900 mai i ngā taha e rua.

$$324-61y^{2}-900=0$$

Tangohia te 900 i te 324, ka -576.

$$-576-61y^{2}=0$$

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.

$$-61y^{2}-576=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -61 mō a, 0 mō b, me -576 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-61\right)\left(-576\right)}}{2\left(-61\right)}$$

Pūrua 0.

$$y=\frac{0±\sqrt{-4\left(-61\right)\left(-576\right)}}{2\left(-61\right)}$$

Whakareatia -4 ki te -61.

$$y=\frac{0±\sqrt{244\left(-576\right)}}{2\left(-61\right)}$$

Whakareatia 244 ki te -576.

$$y=\frac{0±\sqrt{-140544}}{2\left(-61\right)}$$

Tuhia te pūtakerua o te -140544.

$$y=\frac{0±48\sqrt{61}i}{2\left(-61\right)}$$

Whakareatia 2 ki te -61.

$$y=\frac{0±48\sqrt{61}i}{-122}$$

Nā, me whakaoti te whārite y=\frac{0±48\sqrt{61}i}{-122} ina he tāpiri te ±.

$$y=-\frac{24\sqrt{61}i}{61}$$

Nā, me whakaoti te whārite y=\frac{0±48\sqrt{61}i}{-122} ina he tango te ±.

$$y=\frac{24\sqrt{61}i}{61}$$

Kua oti te whārite te whakatau.

$$y=-\frac{24\sqrt{61}i}{61} y=\frac{24\sqrt{61}i}{61}$$