Whakaoti i te 1000+x^2=500

$$1000 + x ^ { 2 } = 500$$

Whakaoti mō x (complex solution)

$$x=-10\sqrt{5}i\approx -0-22.360679775i$$

$$x=10\sqrt{5}i\approx 22.360679775i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 1000 mai i ngā taha e rua.

$$x^{2}=500-1000$$

Tangohia te 1000 i te 500, ka -500.

$$x^{2}=-500$$

Kua oti te whārite te whakatau.

$$x=10\sqrt{5}i x=-10\sqrt{5}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 500 mai i ngā taha e rua.

$$1000+x^{2}-500=0$$

Tangohia te 500 i te 1000, ka 500.

$$500+x^{2}=0$$

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.

$$x^{2}+500=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me 500 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 500}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 500}}{2}$$

Whakareatia -4 ki te 500.

$$x=\frac{0±\sqrt{-2000}}{2}$$

Tuhia te pūtakerua o te -2000.

$$x=\frac{0±20\sqrt{5}i}{2}$$

Nā, me whakaoti te whārite x=\frac{0±20\sqrt{5}i}{2} ina he tāpiri te ±.

$$x=10\sqrt{5}i$$

Nā, me whakaoti te whārite x=\frac{0±20\sqrt{5}i}{2} ina he tango te ±.

$$x=-10\sqrt{5}i$$

Kua oti te whārite te whakatau.

$$x=10\sqrt{5}i x=-10\sqrt{5}i$$