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

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

Solvi għal x

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(7-x\right)^{2}.

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

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(1-y\right)^{2}.

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

Żid 49 u 1 biex tikseb 50.

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

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(3-x\right)^{2}.

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

Żid 9 u 5 biex tikseb 14.

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

Żid 6x maż-żewġ naħat.

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

Ikkombina -14x u 6x biex tikseb -8x.

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

Naqqas x^{2} miż-żewġ naħat.

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

Ikkombina x^{2} u -x^{2} biex tikseb 0.

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

Naqqas 50 miż-żewġ naħat.

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

Naqqas 50 minn 14 biex tikseb -36.

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

Żid 2y maż-żewġ naħat.

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

Naqqas y^{2} miż-żewġ naħat.

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

Ikkombina -y^{2} u -y^{2} biex tikseb -2y^{2}.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'-8.

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

Meta tiddividi b'-8 titneħħa l-multiplikazzjoni b'-8.

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

Iddividi -36-2y^{2}+2y b'-8.

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

Solvi għal y (complex solution)

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

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

Solvi għal y

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

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