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

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

Atrast x

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

Lineāra vienādojuma risināšanas darbības

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(7-x\right)^{2}.

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

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(1-y\right)^{2}.

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

Saskaitiet 49 un 1, lai iegūtu 50.

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

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(3-x\right)^{2}.

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

Saskaitiet 9 un 5, lai iegūtu 14.

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

Pievienot 6x abās pusēs.

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

Savelciet -14x un 6x, lai iegūtu -8x.

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

Atņemiet x^{2} no abām pusēm.

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

Savelciet x^{2} un -x^{2}, lai iegūtu 0.

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

Atņemiet 50 no abām pusēm.

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

Atņemiet 50 no 14, lai iegūtu -36.

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

Pievienot 2y abās pusēs.

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

Atņemiet y^{2} no abām pusēm.

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

Savelciet -y^{2} un -y^{2}, lai iegūtu -2y^{2}.

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

Vienādojums ir standarta formā.

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

Daliet abas puses ar -8.

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

Dalīšana ar -8 atsauc reizināšanu ar -8.

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

Daliet -36-2y^{2}+2y ar -8.

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

Atrast y (complex solution)

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

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

Atrast y

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

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