Whakaoti i te 144/y^2+y^2=40

$$\frac { 144 } { y ^ { 2 } } + y ^ { 2 } = 40$$

Whakaoti mō y

$$y=-2$$

$$y=2$$

$$y=6$$

$$y=-6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te y^{2}.

$$144+y^{2}y^{2}=40y^{2}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 2 kia riro ai te 4.

$$144+y^{4}=40y^{2}$$

Tangohia te 40y^{2} mai i ngā taha e rua.

$$144+y^{4}-40y^{2}=0$$

Whakakapia te t mō te y^{2}.

$$t^{2}-40t+144=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 1 mō te a, te -40 mō te b, me te 144 mō te c i te ture pūrua.

$$t=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\times 1\times 144}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{40±32}{2}$$

Whakaotia te whārite t=\frac{40±32}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=36 t=4$$

I te mea ko y=t^{2}, ka riro ngā otinga mā te arotake i te y=±\sqrt{t} mō ia t.

$$y=6 y=-6 y=2 y=-2$$