Whakaoti i te 4/x^2+45=0

$$\frac{ 4 }{ { x }^{ 2 } } +45=0$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\sqrt{5}i}{15}\approx -0-0.298142397i$$

$$x=\frac{2\sqrt{5}i}{15}\approx 0.298142397i$$

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^{2}.

$$4+x^{2}\times 45=0$$

Tangohia te 4 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}\times 45=-4$$

Whakawehea ngā taha e rua ki te 45.

$$x^{2}=-\frac{4}{45}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{5}i}{15} x=-\frac{2\sqrt{5}i}{15}$$

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^{2}.

$$4+x^{2}\times 45=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$45x^{2}+4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 45 mō a, 0 mō b, me 4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 45\times 4}}{2\times 45}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 45\times 4}}{2\times 45}$$

Whakareatia -4 ki te 45.

$$x=\frac{0±\sqrt{-180\times 4}}{2\times 45}$$

Whakareatia -180 ki te 4.

$$x=\frac{0±\sqrt{-720}}{2\times 45}$$

Tuhia te pūtakerua o te -720.

$$x=\frac{0±12\sqrt{5}i}{2\times 45}$$

Whakareatia 2 ki te 45.

$$x=\frac{0±12\sqrt{5}i}{90}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{5}i}{90} ina he tāpiri te ±.

$$x=\frac{2\sqrt{5}i}{15}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{5}i}{90} ina he tango te ±.

$$x=-\frac{2\sqrt{5}i}{15}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{5}i}{15} x=-\frac{2\sqrt{5}i}{15}$$