Datrys (7-x)^2+(1-y)^2=(3-x)^2+(5-y^2)

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

Datrys ar gyfer x

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

Camau ar gyfer Datrys Hafaliad Llinol

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(7-x\right)^{2}.

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

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(1-y\right)^{2}.

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

Adio 49 a 1 i gael 50.

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

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(3-x\right)^{2}.

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

Adio 9 a 5 i gael 14.

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

Ychwanegu 6x at y ddwy ochr.

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

Cyfuno -14x a 6x i gael -8x.

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

Tynnu x^{2} o'r ddwy ochr.

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

Cyfuno x^{2} a -x^{2} i gael 0.

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

Tynnu 50 o'r ddwy ochr.

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

Tynnu 50 o 14 i gael -36.

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

Ychwanegu 2y at y ddwy ochr.

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

Tynnu y^{2} o'r ddwy ochr.

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

Cyfuno -y^{2} a -y^{2} i gael -2y^{2}.

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

Mae'r hafaliad yn y ffurf safonol.

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

Rhannu’r ddwy ochr â -8.

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

Mae rhannu â -8 yn dad-wneud lluosi â -8.

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

Rhannwch -36-2y^{2}+2y â -8.

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

Datrys ar gyfer y (complex solution)

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

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

Datrys ar gyfer y

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

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