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

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

Whakaoti mō y

$$y = \frac{6 \sqrt{374}}{11} \approx 10.548588876$$

$$y = -\frac{6 \sqrt{374}}{11} \approx -10.548588876$$

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.

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

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

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

Pahekotia te 36y^{2} me -25y^{2}, ka 11y^{2}.

$$11y^{2}-324=900$$

Me tāpiri te 324 ki ngā taha e rua.

$$11y^{2}=900+324$$

Tāpirihia te 900 ki te 324, ka 1224.

$$11y^{2}=1224$$

Whakawehea ngā taha e rua ki te 11.

$$y^{2}=\frac{1224}{11}$$

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

$$y=\frac{6\sqrt{374}}{11} y=-\frac{6\sqrt{374}}{11}$$

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.

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

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

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

Pahekotia te 36y^{2} me -25y^{2}, ka 11y^{2}.

$$11y^{2}-324=900$$

Tangohia te 900 mai i ngā taha e rua.

$$11y^{2}-324-900=0$$

Tangohia te 900 i te -324, ka -1224.

$$11y^{2}-1224=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 11 mō a, 0 mō b, me -1224 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 11\left(-1224\right)}}{2\times 11}$$

Pūrua 0.

$$y=\frac{0±\sqrt{-4\times 11\left(-1224\right)}}{2\times 11}$$

Whakareatia -4 ki te 11.

$$y=\frac{0±\sqrt{-44\left(-1224\right)}}{2\times 11}$$

Whakareatia -44 ki te -1224.

$$y=\frac{0±\sqrt{53856}}{2\times 11}$$

Tuhia te pūtakerua o te 53856.

$$y=\frac{0±12\sqrt{374}}{2\times 11}$$

Whakareatia 2 ki te 11.

$$y=\frac{0±12\sqrt{374}}{22}$$

Nā, me whakaoti te whārite y=\frac{0±12\sqrt{374}}{22} ina he tāpiri te ±.

$$y=\frac{6\sqrt{374}}{11}$$

Nā, me whakaoti te whārite y=\frac{0±12\sqrt{374}}{22} ina he tango te ±.

$$y=-\frac{6\sqrt{374}}{11}$$

Kua oti te whārite te whakatau.

$$y=\frac{6\sqrt{374}}{11} y=-\frac{6\sqrt{374}}{11}$$