Whakaoti i te (x)=x+4+2xquadg:x-x^2

$$( x ) = x + 4 + 2 x \quad g : x - x ^ { 2 }$$

Whakaoti mō g

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

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te x.

$$xx=xx+x\times 4+2xg-x^{2}x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}=xx+x\times 4+2xg-x^{2}x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}=x^{2}+x\times 4+2xg-x^{2}x$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.

$$x^{2}=x^{2}+x\times 4+2xg-x^{3}$$

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

$$x^{2}+x\times 4+2xg-x^{3}=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$x\times 4+2xg-x^{3}=x^{2}-x^{2}$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$x\times 4+2xg-x^{3}=0$$

Tangohia te x\times 4 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2xg-x^{3}=-x\times 4$$

Me tāpiri te x^{3} ki ngā taha e rua.

$$2xg=-x\times 4+x^{3}$$

Whakareatia te -1 ki te 4, ka -4.

$$2xg=-4x+x^{3}$$

He hanga arowhānui tō te whārite.

$$2xg=x^{3}-4x$$

Whakawehea ngā taha e rua ki te 2x.

$$\frac{2xg}{2x}=\frac{x^{3}-4x}{2x}$$

Mā te whakawehe ki te 2x ka wetekia te whakareanga ki te 2x.

$$g=\frac{x^{3}-4x}{2x}$$

Whakawehe x^{3}-4x ki te 2x.

$$g=\frac{x^{2}}{2}-2$$

Whakaoti mō x (complex solution)

$$x=-\sqrt{2\left(g+2\right)}$$

$$x=\sqrt{2\left(g+2\right)}\text{, }g\neq -2$$

Whakaoti mō x

$$x=\sqrt{2\left(g+2\right)}$$

$$x=-\sqrt{2\left(g+2\right)}\text{, }g>-2$$