Whakaoti i te (7-x)^2+(1-y)^2=(3-x)^2+(5-y^2)

$$( 7 - x ) ^ { 2 } + ( 1 - y ) ^ { 2 } = ( 3 - x ) ^ { 2 } + ( 5 - y ^ { 2 } )$$

Whakaoti mō x

$$x=\frac{y^{2}-y+18}{4}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(7-x\right)^{2}.

$$49-14x+x^{2}+\left(1-y\right)^{2}=\left(3-x\right)^{2}+5-y^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(1-y\right)^{2}.

$$49-14x+x^{2}+1-2y+y^{2}=\left(3-x\right)^{2}+5-y^{2}$$

Tāpirihia te 49 ki te 1, ka 50.

$$50-14x+x^{2}-2y+y^{2}=\left(3-x\right)^{2}+5-y^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(3-x\right)^{2}.

$$50-14x+x^{2}-2y+y^{2}=9-6x+x^{2}+5-y^{2}$$

Tāpirihia te 9 ki te 5, ka 14.

$$50-14x+x^{2}-2y+y^{2}=14-6x+x^{2}-y^{2}$$

Me tāpiri te 6x ki ngā taha e rua.

$$50-14x+x^{2}-2y+y^{2}+6x=14+x^{2}-y^{2}$$

Pahekotia te -14x me 6x, ka -8x.

$$50-8x+x^{2}-2y+y^{2}=14+x^{2}-y^{2}$$

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

$$50-8x+x^{2}-2y+y^{2}-x^{2}=14-y^{2}$$

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

$$50-8x-2y+y^{2}=14-y^{2}$$

Tangohia te 50 mai i ngā taha e rua.

$$-8x-2y+y^{2}=14-y^{2}-50$$

Tangohia te 50 i te 14, ka -36.

$$-8x-2y+y^{2}=-36-y^{2}$$

Me tāpiri te 2y ki ngā taha e rua.

$$-8x+y^{2}=-36-y^{2}+2y$$

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

$$-8x=-36-y^{2}+2y-y^{2}$$

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

$$-8x=-36-2y^{2}+2y$$

He hanga arowhānui tō te whārite.

$$-8x=-2y^{2}+2y-36$$

Whakawehea ngā taha e rua ki te -8.

$$\frac{-8x}{-8}=\frac{-2y^{2}+2y-36}{-8}$$

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

$$x=\frac{-2y^{2}+2y-36}{-8}$$

Whakawehe -36-2y^{2}+2y ki te -8.

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

Whakaoti mō y (complex solution)

$$y=\frac{\sqrt{16x-71}+1}{2}$$

$$y=\frac{-\sqrt{16x-71}+1}{2}$$

Whakaoti mō y

$$y=\frac{\sqrt{16x-71}+1}{2}$$

$$y=\frac{-\sqrt{16x-71}+1}{2}\text{, }x\geq \frac{71}{16}$$