Whakaoti i te 2=3x(2-j^2)

$$2 = 3 x ( 2 - j ^ { 2 } )$$

Whakaoti mō x (complex solution)

$$x=-\frac{2}{3\left(j^{2}-2\right)}$$

$$j\neq -\sqrt{2}\text{ and }j\neq \sqrt{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te 2-j^{2}.

$$2=6x-3xj^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$6x-3xj^{2}=2$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(6-3j^{2}\right)x=2$$

Whakawehea ngā taha e rua ki te 6-3j^{2}.

$$\frac{\left(6-3j^{2}\right)x}{6-3j^{2}}=\frac{2}{6-3j^{2}}$$

Mā te whakawehe ki te 6-3j^{2} ka wetekia te whakareanga ki te 6-3j^{2}.

$$x=\frac{2}{6-3j^{2}}$$

Whakawehe 2 ki te 6-3j^{2}.

$$x=\frac{2}{3\left(2-j^{2}\right)}$$

Whakaoti mō x

$$x=-\frac{2}{3\left(j^{2}-2\right)}$$

$$|j|\neq \sqrt{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te 2-j^{2}.

$$2=6x-3xj^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$6x-3xj^{2}=2$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(6-3j^{2}\right)x=2$$

Whakawehea ngā taha e rua ki te 6-3j^{2}.

$$\frac{\left(6-3j^{2}\right)x}{6-3j^{2}}=\frac{2}{6-3j^{2}}$$

Mā te whakawehe ki te 6-3j^{2} ka wetekia te whakareanga ki te 6-3j^{2}.

$$x=\frac{2}{6-3j^{2}}$$

Whakawehe 2 ki te 6-3j^{2}.

$$x=\frac{2}{3\left(2-j^{2}\right)}$$

Whakaoti mō j (complex solution)

$$j=-\frac{\sqrt{18-\frac{6}{x}}}{3}$$

$$j=\frac{\sqrt{18-\frac{6}{x}}}{3}\text{, }x\neq 0$$

Whakaoti mō j

$$j=\frac{\sqrt{18-\frac{6}{x}}}{3}$$

$$j=-\frac{\sqrt{18-\frac{6}{x}}}{3}\text{, }x\geq \frac{1}{3}\text{ or }x<0$$