Whakaoti i te -5x^-4=5/x^6

$$- 5 x ^ { - 4 } = \frac { 5 } { x ^ { 6 } }$$

Whakaoti mō x (complex solution)

$$x=i$$

$$x=-i$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x^{6}.

$$-5x^{-4}x^{6}=5$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te -4 me te 6 kia riro ai te 2.

$$-5x^{2}=5$$

Whakawehea ngā taha e rua ki te -5.

$$x^{2}=\frac{5}{-5}$$

Whakawehea te 5 ki te -5, kia riro ko -1.

$$x^{2}=-1$$

Kua oti te whārite te whakatau.

$$x=i x=-i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x^{6}.

$$-5x^{-4}x^{6}=5$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te -4 me te 6 kia riro ai te 2.

$$-5x^{2}=5$$

Tangohia te 5 mai i ngā taha e rua.

$$-5x^{2}-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 0 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\left(-5\right)}}{2\left(-5\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\left(-5\right)}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$x=\frac{0±\sqrt{20\left(-5\right)}}{2\left(-5\right)}$$

Whakareatia 20 ki te -5.

$$x=\frac{0±\sqrt{-100}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te -100.

$$x=\frac{0±10i}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$x=\frac{0±10i}{-10}$$

Nā, me whakaoti te whārite x=\frac{0±10i}{-10} ina he tāpiri te ±.

$$x=-i$$

Nā, me whakaoti te whārite x=\frac{0±10i}{-10} ina he tango te ±.

$$x=i$$

Kua oti te whārite te whakatau.

$$x=-i x=i$$