Whakaoti i te 4/b^2+4+25/9b^2=1

$$\frac { 4 } { b ^ { 2 } + 4 } + \frac { 25 } { 9 b ^ { 2 } } = 1$$

Whakaoti mō b

$$b=\sqrt{5}\approx 2.236067977$$

$$b=-\sqrt{5}\approx -2.236067977$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe b ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 9b^{2}\left(b^{2}+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o b^{2}+4,9b^{2}.

$$9b^{2}\times 4+\left(b^{2}+4\right)\times 25=9b^{2}\left(b^{2}+4\right)$$

Whakareatia te 9 ki te 4, ka 36.

$$36b^{2}+\left(b^{2}+4\right)\times 25=9b^{2}\left(b^{2}+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te b^{2}+4 ki te 25.

$$36b^{2}+25b^{2}+100=9b^{2}\left(b^{2}+4\right)$$

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

$$61b^{2}+100=9b^{2}\left(b^{2}+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9b^{2} ki te b^{2}+4.

$$61b^{2}+100=9b^{4}+36b^{2}$$

Tangohia te 9b^{4} mai i ngā taha e rua.

$$61b^{2}+100-9b^{4}=36b^{2}$$

Tangohia te 36b^{2} mai i ngā taha e rua.

$$61b^{2}+100-9b^{4}-36b^{2}=0$$

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

$$25b^{2}+100-9b^{4}=0$$

Whakakapia te t mō te b^{2}.

$$-9t^{2}+25t+100=0$$

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 -9 mō te a, te 25 mō te b, me te 100 mō te c i te ture pūrua.

$$t=\frac{-25±\sqrt{25^{2}-4\left(-9\right)\times 100}}{-9\times 2}$$

Mahia ngā tātaitai.

$$t=\frac{-25±65}{-18}$$

Whakaotia te whārite t=\frac{-25±65}{-18} ina he tōrunga te ±, ina he tōraro te ±.

$$t=-\frac{20}{9} t=5$$

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

$$b=\sqrt{5} b=-\sqrt{5}$$