Whakaoti i te 15x^{2}z^3+20x^2z^2=5xz^2(3xz+4x)

$$15 x ^ { 2 } z ^ { 3 } + 20 x ^ { 2 } z ^ { 2 } = 5 x z ^ { 2 } ( 3 x z + 4 x )$$

Whakaoti mō x (complex solution)

$$x\in \mathrm{C}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 5xz^{2} ki te 3xz+4x.

$$15x^{2}z^{3}+20x^{2}z^{2}=15x^{2}z^{3}+20x^{2}z^{2}$$

Tangohia te 15x^{2}z^{3} mai i ngā taha e rua.

$$15x^{2}z^{3}+20x^{2}z^{2}-15x^{2}z^{3}=20x^{2}z^{2}$$

Pahekotia te 15x^{2}z^{3} me -15x^{2}z^{3}, ka 0.

$$20x^{2}z^{2}=20x^{2}z^{2}$$

Tangohia te 20x^{2}z^{2} mai i ngā taha e rua.

$$20x^{2}z^{2}-20x^{2}z^{2}=0$$

Pahekotia te 20x^{2}z^{2} me -20x^{2}z^{2}, ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

$$x\in \mathrm{C}$$

Whakaoti mō z (complex solution)

$$z\in \mathrm{C}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 5xz^{2} ki te 3xz+4x.

$$15x^{2}z^{3}+20x^{2}z^{2}=15x^{2}z^{3}+20x^{2}z^{2}$$

Tangohia te 15x^{2}z^{3} mai i ngā taha e rua.

$$15x^{2}z^{3}+20x^{2}z^{2}-15x^{2}z^{3}=20x^{2}z^{2}$$

Pahekotia te 15x^{2}z^{3} me -15x^{2}z^{3}, ka 0.

$$20x^{2}z^{2}=20x^{2}z^{2}$$

Tangohia te 20x^{2}z^{2} mai i ngā taha e rua.

$$20x^{2}z^{2}-20x^{2}z^{2}=0$$

Pahekotia te 20x^{2}z^{2} me -20x^{2}z^{2}, ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi z ahakoa.

$$z\in \mathrm{C}$$

Whakaoti mō x

$$x\in \mathrm{R}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 5xz^{2} ki te 3xz+4x.

$$15x^{2}z^{3}+20x^{2}z^{2}=15x^{2}z^{3}+20x^{2}z^{2}$$

Tangohia te 15x^{2}z^{3} mai i ngā taha e rua.

$$15x^{2}z^{3}+20x^{2}z^{2}-15x^{2}z^{3}=20x^{2}z^{2}$$

Pahekotia te 15x^{2}z^{3} me -15x^{2}z^{3}, ka 0.

$$20x^{2}z^{2}=20x^{2}z^{2}$$

Tangohia te 20x^{2}z^{2} mai i ngā taha e rua.

$$20x^{2}z^{2}-20x^{2}z^{2}=0$$

Pahekotia te 20x^{2}z^{2} me -20x^{2}z^{2}, ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

$$x\in \mathrm{R}$$

Whakaoti mō z

$$z\in \mathrm{R}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 5xz^{2} ki te 3xz+4x.

$$15x^{2}z^{3}+20x^{2}z^{2}=15x^{2}z^{3}+20x^{2}z^{2}$$

Tangohia te 15x^{2}z^{3} mai i ngā taha e rua.

$$15x^{2}z^{3}+20x^{2}z^{2}-15x^{2}z^{3}=20x^{2}z^{2}$$

Pahekotia te 15x^{2}z^{3} me -15x^{2}z^{3}, ka 0.

$$20x^{2}z^{2}=20x^{2}z^{2}$$

Tangohia te 20x^{2}z^{2} mai i ngā taha e rua.

$$20x^{2}z^{2}-20x^{2}z^{2}=0$$

Pahekotia te 20x^{2}z^{2} me -20x^{2}z^{2}, ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi z ahakoa.

$$z\in \mathrm{R}$$