Whakaoti i te 3x+A^4/9+A^2=9-A^2

$$3 x + \frac { A ^ { 4 } } { 9 + A ^ { 2 } } = 9 - A ^ { 2 }$$

Whakaoti mō x (complex solution)

$$x=-\frac{2A^{4}-81}{3\left(A^{2}+9\right)}$$

$$A\neq -3i\text{ and }A\neq 3i$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te \left(A-3i\right)\left(A+3i\right).

$$3x\left(A-3i\right)\left(A+3i\right)+A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te A-3i.

$$\left(3xA-9ix\right)\left(A+3i\right)+A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3xA-9ix ki te A+3i ka whakakotahi i ngā kupu rite.

$$3xA^{2}+27x+A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te A-3i ki te A+3i ka whakakotahi i ngā kupu rite.

$$3xA^{2}+27x+A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te A^{2}+9 ki te 9.

$$3xA^{2}+27x+A^{4}=9A^{2}+81-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -A^{2} ki te A-3i.

$$3xA^{2}+27x+A^{4}=9A^{2}+81+\left(-A^{3}+3iA^{2}\right)\left(A+3i\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -A^{3}+3iA^{2} ki te A+3i ka whakakotahi i ngā kupu rite.

$$3xA^{2}+27x+A^{4}=9A^{2}+81-A^{4}-9A^{2}$$

Pahekotia te 9A^{2} me -9A^{2}, ka 0.

$$3xA^{2}+27x+A^{4}=81-A^{4}$$

Tangohia te A^{4} mai i ngā taha e rua.

$$3xA^{2}+27x=81-A^{4}-A^{4}$$

Pahekotia te -A^{4} me -A^{4}, ka -2A^{4}.

$$3xA^{2}+27x=81-2A^{4}$$

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

$$\left(3A^{2}+27\right)x=81-2A^{4}$$

Whakawehea ngā taha e rua ki te 3A^{2}+27.

$$\frac{\left(3A^{2}+27\right)x}{3A^{2}+27}=\frac{81-2A^{4}}{3A^{2}+27}$$

Mā te whakawehe ki te 3A^{2}+27 ka wetekia te whakareanga ki te 3A^{2}+27.

$$x=\frac{81-2A^{4}}{3A^{2}+27}$$

Whakawehe 81-2A^{4} ki te 3A^{2}+27.

$$x=\frac{81-2A^{4}}{3\left(A^{2}+9\right)}$$

Whakaoti mō x

$$x=-\frac{2A^{4}-81}{3\left(A^{2}+9\right)}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te A^{2}+9.

$$3x\left(A^{2}+9\right)+A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te A^{2}+9.

$$3xA^{2}+27x+A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te A^{2}+9 ki te 9.

$$3xA^{2}+27x+A^{4}=9A^{2}+81-A^{2}\left(A^{2}+9\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -A^{2} ki te A^{2}+9.

$$3xA^{2}+27x+A^{4}=9A^{2}+81-A^{4}-9A^{2}$$

Pahekotia te 9A^{2} me -9A^{2}, ka 0.

$$3xA^{2}+27x+A^{4}=81-A^{4}$$

Tangohia te A^{4} mai i ngā taha e rua.

$$3xA^{2}+27x=81-A^{4}-A^{4}$$

Pahekotia te -A^{4} me -A^{4}, ka -2A^{4}.

$$3xA^{2}+27x=81-2A^{4}$$

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

$$\left(3A^{2}+27\right)x=81-2A^{4}$$

Whakawehea ngā taha e rua ki te 3A^{2}+27.

$$\frac{\left(3A^{2}+27\right)x}{3A^{2}+27}=\frac{81-2A^{4}}{3A^{2}+27}$$

Mā te whakawehe ki te 3A^{2}+27 ka wetekia te whakareanga ki te 3A^{2}+27.

$$x=\frac{81-2A^{4}}{3A^{2}+27}$$

Whakawehe 81-2A^{4} ki te 3A^{2}+27.

$$x=\frac{81-2A^{4}}{3\left(A^{2}+9\right)}$$

Whakaoti mō A (complex solution)

$$A=\frac{\sqrt{3\sqrt{x^{2}-24x+72}-3x}}{2}$$

$$A=-\frac{\sqrt{3\sqrt{x^{2}-24x+72}-3x}}{2}$$

$$A=-\frac{\sqrt{-3\sqrt{x^{2}-24x+72}-3x}}{2}$$

$$A=\frac{\sqrt{-3\sqrt{x^{2}-24x+72}-3x}}{2}$$

Whakaoti mō A

$$A=-\frac{\sqrt{3\left(\sqrt{x^{2}-24x+72}-x\right)}}{2}$$

$$A=\frac{\sqrt{3\left(\sqrt{x^{2}-24x+72}-x\right)}}{2}\text{, }x\leq 3$$