Question

二元二次方程组如何用计算机解

（a-x)*2+(b-y)*2=c*2
(d-x)*2+(e-y)*2=f*2
*2是平方的意思
a,b,c,d,e,f是常数，求x,y
最好能编个小软件或者用excel编辑，求高手解决，不胜感激！！

Answer 1

x =
-1/2*(-1/(4*e^2+4*a^2-8*e*b-8*a*d+4*b^2+4*d^2)*(-8*a*d*b-4*e*b^2-8*a*d*e-4*c^2*b+4*b^3-4*e^2*b+4*a^2*e+4*f^2*b-4*e*f^2+4*e^3+4*d^2*e+4*d^2*b+4*a^2*b+4*e*c^2+4*(24*a^2*d^2*b*e-8*a*d^3*c^2-4*a*d*f^2*c^2-8*a*d*b^3*e-e^4*d^2-e^4*a^2+2*e^4*a*d-4*a*d*b^2*c^2+12*a*d*b^2*e^2-16*a^3*d*b*e-4*a*d*b^2*f^2-8*a*d*b*e^3-16*a*d^3*b*e-4*a*d*e^2*f^2-4*a*d*e^2*c^2-4*c^2*b*a^2*e-4*c^2*b*d^2*e-4*a^2*e*f^2*b-12*a^2*d^2*b^2+2*a*d*b^4+8*a^3*d*b^2-6*e^2*b^2*a^2-6*e^2*b^2*d^2+4*e*b^3*d^2+4*e*b^3*a^2-12*a^2*d^2*e^2+8*a^3*d*e^2+8*a*d^3*e^2+2*c^2*b^2*d^2+2*c^2*b^2*a^2+4*e^3*b*a^2+4*e^3*b*d^2+2*a^2*e^2*f^2+4*a^4*e*b+2*a^2*e^2*c^2-b^4*d^2-b^4*a^2-2*a^4*e^2-a^6-d^6+8*a*d*b*e*f^2+8*a*d^3*b^2+8*a*d*b*e*c^2+2*a*d*f^4+2*a*d*c^4-8*a*d^3*f^2+2*d^2*f^2*c^2-4*f^2*b*d^2*e+2*f^2*b^2*d^2+2*f^2*b^2*a^2+2*e^2*f^2*d^2+4*d^4*e*b+2*d^2*e^2*c^2+12*a^2*d^2*c^2+2*a^2*f^2*c^2-8*a^3*d*f^2-8*a^3*d*c^2+12*a^2*d^2*f^2-2*d^4*e^2-2*d^4*b^2-2*a^4*b^2+2*a^4*f^2-a^2*f^4+2*a^4*c^2-15*a^2*d^4-a^2*c^4-15*a^4*d^2+20*a^3*d^3+6*a^5*d+6*a*d^5+2*d^4*c^2-d^2*f^4-d^2*c^4+2*d^4*f^2)^(1/2))*e+1/(4*e^2+4*a^2-8*e*b-8*a*d+4*b^2+4*d^2)*(-8*a*d*b-4*e*b^2-8*a*d*e-4*c^2*b+4*b^3-4*e^2*b+4*a^2*e+4*f^2*b-4*e*f^2+4*e^3+4*d^2*e+4*d^2*b+4*a^2*b+4*e*c^2+4*(24*a^2*d^2*b*e-8*a*d^3*c^2-4*a*d*f^2*c^2-8*a*d*b^3*e-e^4*d^2-e^4*a^2+2*e^4*a*d-4*a*d*b^2*c^2+12*a*d*b^2*e^2-16*a^3*d*b*e-4*a*d*b^2*f^2-8*a*d*b*e^3-16*a*d^3*b*e-4*a*d*e^2*f^2-4*a*d*e^2*c^2-4*c^2*b*a^2*e-4*c^2*b*d^2*e-4*a^2*e*f^2*b-12*a^2*d^2*b^2+2*a*d*b^4+8*a^3*d*b^2-6*e^2*b^2*a^2-6*e^2*b^2*d^2+4*e*b^3*d^2+4*e*b^3*a^2-12*a^2*d^2*e^2+8*a^3*d*e^2+8*a*d^3*e^2+2*c^2*b^2*d^2+2*c^2*b^2*a^2+4*e^3*b*a^2+4*e^3*b*d^2+2*a^2*e^2*f^2+4*a^4*e*b+2*a^2*e^2*c^2-b^4*d^2-b^4*a^2-2*a^4*e^2-a^6-d^6+8*a*d*b*e*f^2+8*a*d^3*b^2+8*a*d*b*e*c^2+2*a*d*f^4+2*a*d*c^4-8*a*d^3*f^2+2*d^2*f^2*c^2-4*f^2*b*d^2*e+2*f^2*b^2*d^2+2*f^2*b^2*a^2+2*e^2*f^2*d^2+4*d^4*e*b+2*d^2*e^2*c^2+12*a^2*d^2*c^2+2*a^2*f^2*c^2-8*a^3*d*f^2-8*a^3*d*c^2+12*a^2*d^2*f^2-2*d^4*e^2-2*d^4*b^2-2*a^4*b^2+2*a^4*f^2-a^2*f^4+2*a^4*c^2-15*a^2*d^4-a^2*c^4-15*a^4*d^2+20*a^3*d^3+6*a^5*d+6*a*d^5+2*d^4*c^2-d^2*f^4-d^2*c^4+2*d^4*f^2)^(1/2))*b+d^2+e^2-f^2-a^2-b^2+c^2)/(-d+a)

-1/2*(-1/(4*e^2+4*a^2-8*e*b-8*a*d+4*b^2+4*d^2)*(-8*a*d*b-4*e*b^2-8*a*d*e-4*c^2*b+4*b^3-4*e^2*b+4*a^2*e+4*f^2*b-4*e*f^2+4*e^3+4*d^2*e+4*d^2*b+4*a^2*b+4*e*c^2-4*(24*a^2*d^2*b*e-8*a*d^3*c^2-4*a*d*f^2*c^2-8*a*d*b^3*e-e^4*d^2-e^4*a^2+2*e^4*a*d-4*a*d*b^2*c^2+12*a*d*b^2*e^2-16*a^3*d*b*e-4*a*d*b^2*f^2-8*a*d*b*e^3-16*a*d^3*b*e-4*a*d*e^2*f^2-4*a*d*e^2*c^2-4*c^2*b*a^2*e-4*c^2*b*d^2*e-4*a^2*e*f^2*b-12*a^2*d^2*b^2+2*a*d*b^4+8*a^3*d*b^2-6*e^2*b^2*a^2-6*e^2*b^2*d^2+4*e*b^3*d^2+4*e*b^3*a^2-12*a^2*d^2*e^2+8*a^3*d*e^2+8*a*d^3*e^2+2*c^2*b^2*d^2+2*c^2*b^2*a^2+4*e^3*b*a^2+4*e^3*b*d^2+2*a^2*e^2*f^2+4*a^4*e*b+2*a^2*e^2*c^2-b^4*d^2-b^4*a^2-2*a^4*e^2-a^6-d^6+8*a*d*b*e*f^2+8*a*d^3*b^2+8*a*d*b*e*c^2+2*a*d*f^4+2*a*d*c^4-8*a*d^3*f^2+2*d^2*f^2*c^2-4*f^2*b*d^2*e+2*f^2*b^2*d^2+2*f^2*b^2*a^2+2*e^2*f^2*d^2+4*d^4*e*b+2*d^2*e^2*c^2+12*a^2*d^2*c^2+2*a^2*f^2*c^2-8*a^3*d*f^2-8*a^3*d*c^2+12*a^2*d^2*f^2-2*d^4*e^2-2*d^4*b^2-2*a^4*b^2+2*a^4*f^2-a^2*f^4+2*a^4*c^2-15*a^2*d^4-a^2*c^4-15*a^4*d^2+20*a^3*d^3+6*a^5*d+6*a*d^5+2*d^4*c^2-d^2*f^4-d^2*c^4+2*d^4*f^2)^(1/2))*e+1/(4*e^2+4*a^2-8*e*b-8*a*d+4*b^2+4*d^2)*(-8*a*d*b-4*e*b^2-8*a*d*e-4*c^2*b+4*b^3-4*e^2*b+4*a^2*e+4*f^2*b-4*e*f^2+4*e^3+4*d^2*e+4*d^2*b+4*a^2*b+4*e*c^2-4*(24*a^2*d^2*b*e-8*a*d^3*c^2-4*a*d*f^2*c^2-8*a*d*b^3*e-e^4*d^2-e^4*a^2+2*e^4*a*d-4*a*d*b^2*c^2+12*a*d*b^2*e^2-16*a^3*d*b*e-4*a*d*b^2*f^2-8*a*d*b*e^3-16*a*d^3*b*e-4*a*d*e^2*f^2-4*a*d*e^2*c^2-4*c^2*b*a^2*e-4*c^2*b*d^2*e-4*a^2*e*f^2*b-12*a^2*d^2*b^2+2*a*d*b^4+8*a^3*d*b^2-6*e^2*b^2*a^2-6*e^2*b^2*d^2+4*e*b^3*d^2+4*e*b^3*a^2-12*a^2*d^2*e^2+8*a^3*d*e^2+8*a*d^3*e^2+2*c^2*b^2*d^2+2*c^2*b^2*a^2+4*e^3*b*a^2+4*e^3*b*d^2+2*a^2*e^2*f^2+4*a^4*e*b+2*a^2*e^2*c^2-b^4*d^2-b^4*a^2-2*a^4*e^2-a^6-d^6+8*a*d*b*e*f^2+8*a*d^3*b^2+8*a*d*b*e*c^2+2*a*d*f^4+2*a*d*c^4-8*a*d^3*f^2+2*d^2*f^2*c^2-4*f^2*b*d^2*e+2*f^2*b^2*d^2+2*f^2*b^2*a^2+2*e^2*f^2*d^2+4*d^4*e*b+2*d^2*e^2*c^2+12*a^2*d^2*c^2+2*a^2*f^2*c^2-8*a^3*d*f^2-8*a^3*d*c^2+12*a^2*d^2*f^2-2*d^4*e^2-2*d^4*b^2-2*a^4*b^2+2*a^4*f^2-a^2*f^4+2*a^4*c^2-15*a^2*d^4-a^2*c^4-15*a^4*d^2+20*a^3*d^3+6*a^5*d+6*a*d^5+2*d^4*c^2-d^2*f^4-d^2*c^4+2*d^4*f^2)^(1/2))*b+d^2+e^2-f^2-a^2-b^2+c^2)/(-d+a)

y =

1/2/(4*e^2+4*a^2-8*e*b-8*a*d+4*b^2+4*d^2)*(-8*a*d*b-4*e*b^2-8*a*d*e-4*c^2*b+4*b^3-4*e^2*b+4*a^2*e+4*f^2*b-4*e*f^2+4*e^3+4*d^2*e+4*d^2*b+4*a^2*b+4*e*c^2+4*(24*a^2*d^2*b*e-8*a*d^3*c^2-4*a*d*f^2*c^2-8*a*d*b^3*e-e^4*d^2-e^4*a^2+2*e^4*a*d-4*a*d*b^2*c^2+12*a*d*b^2*e^2-16*a^3*d*b*e-4*a*d*b^2*f^2-8*a*d*b*e^3-16*a*d^3*b*e-4*a*d*e^2*f^2-4*a*d*e^2*c^2-4*c^2*b*a^2*e-4*c^2*b*d^2*e-4*a^2*e*f^2*b-12*a^2*d^2*b^2+2*a*d*b^4+8*a^3*d*b^2-6*e^2*b^2*a^2-6*e^2*b^2*d^2+4*e*b^3*d^2+4*e*b^3*a^2-12*a^2*d^2*e^2+8*a^3*d*e^2+8*a*d^3*e^2+2*c^2*b^2*d^2+2*c^2*b^2*a^2+4*e^3*b*a^2+4*e^3*b*d^2+2*a^2*e^2*f^2+4*a^4*e*b+2*a^2*e^2*c^2-b^4*d^2-b^4*a^2-2*a^4*e^2-a^6-d^6+8*a*d*b*e*f^2+8*a*d^3*b^2+8*a*d*b*e*c^2+2*a*d*f^4+2*a*d*c^4-8*a*d^3*f^2+2*d^2*f^2*c^2-4*f^2*b*d^2*e+2*f^2*b^2*d^2+2*f^2*b^2*a^2+2*e^2*f^2*d^2+4*d^4*e*b+2*d^2*e^2*c^2+12*a^2*d^2*c^2+2*a^2*f^2*c^2-8*a^3*d*f^2-8*a^3*d*c^2+12*a^2*d^2*f^2-2*d^4*e^2-2*d^4*b^2-2*a^4*b^2+2*a^4*f^2-a^2*f^4+2*a^4*c^2-15*a^2*d^4-a^2*c^4-15*a^4*d^2+20*a^3*d^3+6*a^5*d+6*a*d^5+2*d^4*c^2-d^2*f^4-d^2*c^4+2*d^4*f^2)^(1/2))

1/2/(4*e^2+4*a^2-8*e*b-8*a*d+4*b^2+4*d^2)*(-8*a*d*b-4*e*b^2-8*a*d*e-4*c^2*b+4*b^3-4*e^2*b+4*a^2*e+4*f^2*b-4*e*f^2+4*e^3+4*d^2*e+4*d^2*b+4*a^2*b+4*e*c^2-4*(24*a^2*d^2*b*e-8*a*d^3*c^2-4*a*d*f^2*c^2-8*a*d*b^3*e-e^4*d^2-e^4*a^2+2*e^4*a*d-4*a*d*b^2*c^2+12*a*d*b^2*e^2-16*a^3*d*b*e-4*a*d*b^2*f^2-8*a*d*b*e^3-16*a*d^3*b*e-4*a*d*e^2*f^2-4*a*d*e^2*c^2-4*c^2*b*a^2*e-4*c^2*b*d^2*e-4*a^2*e*f^2*b-12*a^2*d^2*b^2+2*a*d*b^4+8*a^3*d*b^2-6*e^2*b^2*a^2-6*e^2*b^2*d^2+4*e*b^3*d^2+4*e*b^3*a^2-12*a^2*d^2*e^2+8*a^3*d*e^2+8*a*d^3*e^2+2*c^2*b^2*d^2+2*c^2*b^2*a^2+4*e^3*b*a^2+4*e^3*b*d^2+2*a^2*e^2*f^2+4*a^4*e*b+2*a^2*e^2*c^2-b^4*d^2-b^4*a^2-2*a^4*e^2-a^6-d^6+8*a*d*b*e*f^2+8*a*d^3*b^2+8*a*d*b*e*c^2+2*a*d*f^4+2*a*d*c^4-8*a*d^3*f^2+2*d^2*f^2*c^2-4*f^2*b*d^2*e+2*f^2*b^2*d^2+2*f^2*b^2*a^2+2*e^2*f^2*d^2+4*d^4*e*b+2*d^2*e^2*c^2+12*a^2*d^2*c^2+2*a^2*f^2*c^2-8*a^3*d*f^2-8*a^3*d*c^2+12*a^2*d^2*f^2-2*d^4*e^2-2*d^4*b^2-2*a^4*b^2+2*a^4*f^2-a^2*f^4+2*a^4*c^2-15*a^2*d^4-a^2*c^4-15*a^4*d^2+20*a^3*d^3+6*a^5*d+6*a*d^5+2*d^4*c^2-d^2*f^4-d^2*c^4+2*d^4*f^2)^(1/2))

有两个点。把a替换为a1...，f替换为f1，然后在单元格中输入a到f的值就可以了。