Whakaoti i te 4x^2+2=1

$$4 x ^ { 2 } + 2 = 1$$

Whakaoti mō x (complex solution)

$$x=-\frac{1}{2}i=-0.5i$$

$$x=\frac{1}{2}i=0.5i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 2 mai i ngā taha e rua.

$$4x^{2}=1-2$$

Tangohia te 2 i te 1, ka -1.

$$4x^{2}=-1$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=-\frac{1}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{2}i x=-\frac{1}{2}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 1 mai i ngā taha e rua.

$$4x^{2}+2-1=0$$

Tangohia te 1 i te 2, ka 1.

$$4x^{2}+1=0$$

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

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

Pūrua 0.

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

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16}}{2\times 4}$$

Tuhia te pūtakerua o te -16.

$$x=\frac{0±4i}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±4i}{8}$$

Nā, me whakaoti te whārite x=\frac{0±4i}{8} ina he tāpiri te ±.

$$x=\frac{1}{2}i$$

Nā, me whakaoti te whārite x=\frac{0±4i}{8} ina he tango te ±.

$$x=-\frac{1}{2}i$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{2}i x=-\frac{1}{2}i$$