Whakaoti i te 2^2+9x^2=12

$$2 ^ { 2 } + 9 x ^ { 2 } = 12$$

Whakaoti mō x

$$x=\frac{2\sqrt{2}}{3}\approx 0.942809042$$

$$x=-\frac{2\sqrt{2}}{3}\approx -0.942809042$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$4+9x^{2}=12$$

Tangohia te 4 mai i ngā taha e rua.

$$9x^{2}=12-4$$

Tangohia te 4 i te 12, ka 8.

$$9x^{2}=8$$

Whakawehea ngā taha e rua ki te 9.

$$x^{2}=\frac{8}{9}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$x=\frac{2\sqrt{2}}{3} x=-\frac{2\sqrt{2}}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$4+9x^{2}=12$$

Tangohia te 12 mai i ngā taha e rua.

$$4+9x^{2}-12=0$$

Tangohia te 12 i te 4, ka -8.

$$-8+9x^{2}=0$$

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.

$$9x^{2}-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 0 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-8\right)}}{2\times 9}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-8\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{0±\sqrt{-36\left(-8\right)}}{2\times 9}$$

Whakareatia -36 ki te -8.

$$x=\frac{0±\sqrt{288}}{2\times 9}$$

Tuhia te pūtakerua o te 288.

$$x=\frac{0±12\sqrt{2}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{0±12\sqrt{2}}{18}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{2}}{18} ina he tāpiri te ±.

$$x=\frac{2\sqrt{2}}{3}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{2}}{18} ina he tango te ±.

$$x=-\frac{2\sqrt{2}}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{2}}{3} x=-\frac{2\sqrt{2}}{3}$$