Whakaoti i te -x^2(x^2-13)=-42

$$- x ^ { 2 } ( x ^ { 2 } - 13 ) = - 42$$

Whakaoti mō x (complex solution)

$$x=\frac{i\sqrt{2\left(\sqrt{337}-13\right)}}{2}\approx 1.636697857i$$

$$x=-\frac{i\sqrt{2\left(\sqrt{337}-13\right)}}{2}\approx -0-1.636697857i$$

$$x = -\frac{\sqrt{2 {(\sqrt{337} + 13)}}}{2} \approx -3.959643908$$

$$x = \frac{\sqrt{2 {(\sqrt{337} + 13)}}}{2} \approx 3.959643908$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te -x^{2} ki te x^{2}-13.

$$\left(-x^{2}\right)x^{2}-13\left(-x^{2}\right)=-42$$

Whakareatia te -13 ki te -1, ka 13.

$$\left(-x^{2}\right)x^{2}+13x^{2}=-42$$

Me tāpiri te 42 ki ngā taha e rua.

$$\left(-x^{2}\right)x^{2}+13x^{2}+42=0$$

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.

$$-x^{4}+13x^{2}+42=0$$

Whakakapia te t mō te x^{2}.

$$-t^{2}+13t+42=0$$

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 13 mō te b, me te 42 mō te c i te ture pūrua.

$$t=\frac{-13±\sqrt{13^{2}-4\left(-1\right)\times 42}}{-2}$$

Mahia ngā tātaitai.

$$t=\frac{-13±\sqrt{337}}{-2}$$

Whakaotia te whārite t=\frac{-13±\sqrt{337}}{-2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{13-\sqrt{337}}{2} t=\frac{\sqrt{337}+13}{2}$$

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

$$x=-i\sqrt{-\frac{13-\sqrt{337}}{2}} x=i\sqrt{-\frac{13-\sqrt{337}}{2}} x=-\sqrt{\frac{\sqrt{337}+13}{2}} x=\sqrt{\frac{\sqrt{337}+13}{2}}$$

Whakaoti mō x

$$x = -\frac{\sqrt{2 {(\sqrt{337} + 13)}}}{2} \approx -3.959643908$$

$$x = \frac{\sqrt{2 {(\sqrt{337} + 13)}}}{2} \approx 3.959643908$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te -x^{2} ki te x^{2}-13.

$$\left(-x^{2}\right)x^{2}-13\left(-x^{2}\right)=-42$$

Whakareatia te -13 ki te -1, ka 13.

$$\left(-x^{2}\right)x^{2}+13x^{2}=-42$$

Me tāpiri te 42 ki ngā taha e rua.

$$\left(-x^{2}\right)x^{2}+13x^{2}+42=0$$

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.

$$-x^{4}+13x^{2}+42=0$$

Whakakapia te t mō te x^{2}.

$$-t^{2}+13t+42=0$$

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 13 mō te b, me te 42 mō te c i te ture pūrua.

$$t=\frac{-13±\sqrt{13^{2}-4\left(-1\right)\times 42}}{-2}$$

Mahia ngā tātaitai.

$$t=\frac{-13±\sqrt{337}}{-2}$$

Whakaotia te whārite t=\frac{-13±\sqrt{337}}{-2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{13-\sqrt{337}}{2} t=\frac{\sqrt{337}+13}{2}$$

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

$$x=\frac{\sqrt{2\sqrt{337}+26}}{2} x=-\frac{\sqrt{2\sqrt{337}+26}}{2}$$