Whakaoti i te left(4-x-yright)^2=x^2+y^2

$${ \left(4-x-y \right) }^{ 2 } = { x }^{ 2 } + { y }^{ 2 }$$

Whakaoti mō x

$$x=-\frac{4\left(2-y\right)}{y-4}$$

$$y\neq 4$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Pūrua 4-x-y.

$$x^{2}+2xy-8x+y^{2}-8y+16=x^{2}+y^{2}$$

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

$$x^{2}+2xy-8x+y^{2}-8y+16-x^{2}=y^{2}$$

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

$$2xy-8x+y^{2}-8y+16=y^{2}$$

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

$$2xy-8x-8y+16=y^{2}-y^{2}$$

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

$$2xy-8x-8y+16=0$$

Me tāpiri te 8y ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2xy-8x+16=8y$$

Tangohia te 16 mai i ngā taha e rua.

$$2xy-8x=8y-16$$

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

$$\left(2y-8\right)x=8y-16$$

Whakawehea ngā taha e rua ki te 2y-8.

$$\frac{\left(2y-8\right)x}{2y-8}=\frac{8y-16}{2y-8}$$

Mā te whakawehe ki te 2y-8 ka wetekia te whakareanga ki te 2y-8.

$$x=\frac{8y-16}{2y-8}$$

Whakawehe -16+8y ki te 2y-8.

$$x=\frac{4\left(y-2\right)}{y-4}$$

Whakaoti mō y

$$y=-\frac{4\left(2-x\right)}{x-4}$$

$$x\neq 4$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Pūrua 4-x-y.

$$x^{2}+2xy-8x+y^{2}-8y+16=x^{2}+y^{2}$$

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

$$x^{2}+2xy-8x+y^{2}-8y+16-y^{2}=x^{2}$$

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

$$x^{2}+2xy-8x-8y+16=x^{2}$$

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

$$2xy-8x-8y+16=x^{2}-x^{2}$$

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

$$2xy-8x-8y+16=0$$

Me tāpiri te 8x ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2xy-8y+16=8x$$

Tangohia te 16 mai i ngā taha e rua.

$$2xy-8y=8x-16$$

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

$$\left(2x-8\right)y=8x-16$$

Whakawehea ngā taha e rua ki te 2x-8.

$$\frac{\left(2x-8\right)y}{2x-8}=\frac{8x-16}{2x-8}$$

Mā te whakawehe ki te 2x-8 ka wetekia te whakareanga ki te 2x-8.

$$y=\frac{8x-16}{2x-8}$$

Whakawehe -16+8x ki te 2x-8.

$$y=\frac{4\left(x-2\right)}{x-4}$$