Whakaoti i te x^2+7^2=2

$$x ^ { 2 } + 7 ^ { 2 } = 2$$

Whakaoti mō x (complex solution)

$$x=-\sqrt{47}i\approx -0-6.8556546i$$

$$x=\sqrt{47}i\approx 6.8556546i$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$x^{2}+49=2$$

Tangohia te 49 mai i ngā taha e rua.

$$x^{2}=2-49$$

Tangohia te 49 i te 2, ka -47.

$$x^{2}=-47$$

Kua oti te whārite te whakatau.

$$x=\sqrt{47}i x=-\sqrt{47}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$x^{2}+49=2$$

Tangohia te 2 mai i ngā taha e rua.

$$x^{2}+49-2=0$$

Tangohia te 2 i te 49, ka 47.

$$x^{2}+47=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me 47 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 47}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 47}}{2}$$

Whakareatia -4 ki te 47.

$$x=\frac{0±\sqrt{-188}}{2}$$

Tuhia te pūtakerua o te -188.

$$x=\frac{0±2\sqrt{47}i}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{47}i}{2} ina he tāpiri te ±.

$$x=\sqrt{47}i$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{47}i}{2} ina he tango te ±.

$$x=-\sqrt{47}i$$

Kua oti te whārite te whakatau.

$$x=\sqrt{47}i x=-\sqrt{47}i$$