Whakaoti i te -40-5b^2+b^4=0

$$- 40 - 5 b ^ { 2 } + b ^ { 4 } = 0$$

Whakaoti mō b

$$b = -\frac{\sqrt{2 {(\sqrt{185} + 5)}}}{2} \approx -3.049710684$$

$$b = \frac{\sqrt{2 {(\sqrt{185} + 5)}}}{2} \approx 3.049710684$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te b^{2}.

$$t^{2}-5t-40=0$$

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 -5 mō te b, me te -40 mō te c i te ture pūrua.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\left(-40\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{5±\sqrt{185}}{2}$$

Whakaotia te whārite t=\frac{5±\sqrt{185}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{\sqrt{185}+5}{2} t=\frac{5-\sqrt{185}}{2}$$

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

$$b=\frac{\sqrt{2\sqrt{185}+10}}{2} b=-\frac{\sqrt{2\sqrt{185}+10}}{2}$$