二元二次方程组求解 200

方程组如下(x-c)*(x-c)+(d-y)*(d-y)=l*lb*b*x*x+a*a*y*y=a*a*b*b求x,y关于a,b,c,d,l的解... 方程组如下
(x-c)*(x-c)+(d-y)*(d-y)=l*l
b*b*x*x+a*a*y*y=a*a*b*b
求x,y关于a,b,c,d,l的解展开

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#热议# 不吃早饭真的会得胆结石吗？

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过于复杂，利用matlab得出的结果也很长。

x =

(a^2 + c^2 + d^2 - l^2)/(2*c) - (root(2*a^2*b^2*z^4 - b^4*z^4 - a^4*z^4 - 4*a^2*b^2*d*z^3 + 4*b^4*d*z^3 - 2*a^2*b^2*l^2*z^2 + 2*a^2*b^2*d^2*z^2 - 2*a^2*b^2*c^2*z^2 + 2*b^4*l^2*z^2 - 6*b^4*d^2*z^2 - 2*b^4*c^2*z^2 + 2*a^4*b^2*z^2 - 2*a^2*b^4*z^2 - 4*b^4*d*l^2*z + 4*b^4*c^2*d*z + 4*a^2*b^4*d*z + 4*b^4*d^3*z + 2*b^4*d^2*l^2 + 2*b^4*c^2*l^2 + 2*a^2*b^4*l^2 - 2*b^4*c^2*d^2 - 2*a^2*b^4*d^2 + 2*a^2*b^4*c^2 - b^4*l^4 - b^4*d^4 - b^4*c^4 - a^4*b^4, z, 1)*d)/c - ((a^2 - b^2)*root(2*a^2*b^2*z^4 - b^4*z^4 - a^4*z^4 - 4*a^2*b^2*d*z^3 + 4*b^4*d*z^3 - 2*a^2*b^2*l^2*z^2 + 2*a^2*b^2*d^2*z^2 - 2*a^2*b^2*c^2*z^2 + 2*b^4*l^2*z^2 - 6*b^4*d^2*z^2 - 2*b^4*c^2*z^2 + 2*a^4*b^2*z^2 - 2*a^2*b^4*z^2 - 4*b^4*d*l^2*z + 4*b^4*c^2*d*z + 4*a^2*b^4*d*z + 4*b^4*d^3*z + 2*b^4*d^2*l^2 + 2*b^4*c^2*l^2 + 2*a^2*b^4*l^2 - 2*b^4*c^2*d^2 - 2*a^2*b^4*d^2 + 2*a^2*b^4*c^2 - b^4*l^4 - b^4*d^4 - b^4*c^4 - a^4*b^4, z, 1)^2)/(2*b^2*c)

(a^2 + c^2 + d^2 - l^2)/(2*c) - (root(2*a^2*b^2*z^4 - b^4*z^4 - a^4*z^4 - 4*a^2*b^2*d*z^3 + 4*b^4*d*z^3 - 2*a^2*b^2*l^2*z^2 + 2*a^2*b^2*d^2*z^2 - 2*a^2*b^2*c^2*z^2 + 2*b^4*l^2*z^2 - 6*b^4*d^2*z^2 - 2*b^4*c^2*z^2 + 2*a^4*b^2*z^2 - 2*a^2*b^4*z^2 - 4*b^4*d*l^2*z + 4*b^4*c^2*d*z + 4*a^2*b^4*d*z + 4*b^4*d^3*z + 2*b^4*d^2*l^2 + 2*b^4*c^2*l^2 + 2*a^2*b^4*l^2 - 2*b^4*c^2*d^2 - 2*a^2*b^4*d^2 + 2*a^2*b^4*c^2 - b^4*l^4 - b^4*d^4 - b^4*c^4 - a^4*b^4, z, 2)*d)/c - ((a^2 - b^2)*root(2*a^2*b^2*z^4 - b^4*z^4 - a^4*z^4 - 4*a^2*b^2*d*z^3 + 4*b^4*d*z^3 - 2*a^2*b^2*l^2*z^2 + 2*a^2*b^2*d^2*z^2 - 2*a^2*b^2*c^2*z^2 + 2*b^4*l^2*z^2 - 6*b^4*d^2*z^2 - 2*b^4*c^2*z^2 + 2*a^4*b^2*z^2 - 2*a^2*b^4*z^2 - 4*b^4*d*l^2*z + 4*b^4*c^2*d*z + 4*a^2*b^4*d*z + 4*b^4*d^3*z + 2*b^4*d^2*l^2 + 2*b^4*c^2*l^2 + 2*a^2*b^4*l^2 - 2*b^4*c^2*d^2 - 2*a^2*b^4*d^2 + 2*a^2*b^4*c^2 - b^4*l^4 - b^4*d^4 - b^4*c^4 - a^4*b^4, z, 2)^2)/(2*b^2*c)

(a^2 + c^2 + d^2 - l^2)/(2*c) - (root(2*a^2*b^2*z^4 - b^4*z^4 - a^4*z^4 - 4*a^2*b^2*d*z^3 + 4*b^4*d*z^3 - 2*a^2*b^2*l^2*z^2 + 2*a^2*b^2*d^2*z^2 - 2*a^2*b^2*c^2*z^2 + 2*b^4*l^2*z^2 - 6*b^4*d^2*z^2 - 2*b^4*c^2*z^2 + 2*a^4*b^2*z^2 - 2*a^2*b^4*z^2 - 4*b^4*d*l^2*z + 4*b^4*c^2*d*z + 4*a^2*b^4*d*z + 4*b^4*d^3*z + 2*b^4*d^2*l^2 + 2*b^4*c^2*l^2 + 2*a^2*b^4*l^2 - 2*b^4*c^2*d^2 - 2*a^2*b^4*d^2 + 2*a^2*b^4*c^2 - b^4*l^4 - b^4*d^4 - b^4*c^4 - a^4*b^4, z, 3)*d)/c - ((a^2 - b^2)*root(2*a^2*b^2*z^4 - b^4*z^4 - a^4*z^4 - 4*a^2*b^2*d*z^3 + 4*b^4*d*z^3 - 2*a^2*b^2*l^2*z^2 + 2*a^2*b^2*d^2*z^2 - 2*a^2*b^2*c^2*z^2 + 2*b^4*l^2*z^2 - 6*b^4*d^2*z^2 - 2*b^4*c^2*z^2 + 2*a^4*b^2*z^2 - 2*a^2*b^4*z^2 - 4*b^4*d*l^2*z + 4*b^4*c^2*d*z + 4*a^2*b^4*d*z + 4*b^4*d^3*z + 2*b^4*d^2*l^2 + 2*b^4*c^2*l^2 + 2*a^2*b^4*l^2 - 2*b^4*c^2*d^2 - 2*a^2*b^4*d^2 + 2*a^2*b^4*c^2 - b^4*l^4 - b^4*d^4 - b^4*c^4 - a^4*b^4, z, 3)^2)/(2*b^2*c)

(a^2 + c^2 + d^2 - l^2)/(2*c) - (root(2*a^2*b^2*z^4 - b^4*z^4 - a^4*z^4 - 4*a^2*b^2*d*z^3 + 4*b^4*d*z^3 - 2*a^2*b^2*l^2*z^2 + 2*a^2*b^2*d^2*z^2 - 2*a^2*b^2*c^2*z^2 + 2*b^4*l^2*z^2 - 6*b^4*d^2*z^2 - 2*b^4*c^2*z^2 + 2*a^4*b^2*z^2 - 2*a^2*b^4*z^2 - 4*b^4*d*l^2*z + 4*b^4*c^2*d*z + 4*a^2*b^4*d*z + 4*b^4*d^3*z + 2*b^4*d^2*l^2 + 2*b^4*c^2*l^2 + 2*a^2*b^4*l^2 - 2*b^4*c^2*d^2 - 2*a^2*b^4*d^2 + 2*a^2*b^4*c^2 - b^4*l^4 - b^4*d^4 - b^4*c^4 - a^4*b^4, z, 4)*d)/c - ((a^2 - b^2)*root(2*a^2*b^2*z^4 - b^4*z^4 - a^4*z^4 - 4*a^2*b^2*d*z^3 + 4*b^4*d*z^3 - 2*a^2*b^2*l^2*z^2 + 2*a^2*b^2*d^2*z^2 - 2*a^2*b^2*c^2*z^2 + 2*b^4*l^2*z^2 - 6*b^4*d^2*z^2 - 2*b^4*c^2*z^2 + 2*a^4*b^2*z^2 - 2*a^2*b^4*z^2 - 4*b^4*d*l^2*z + 4*b^4*c^2*d*z + 4*a^2*b^4*d*z + 4*b^4*d^3*z + 2*b^4*d^2*l^2 + 2*b^4*c^2*l^2 + 2*a^2*b^4*l^2 - 2*b^4*c^2*d^2 - 2*a^2*b^4*d^2 + 2*a^2*b^4*c^2 - b^4*l^4 - b^4*d^4 - b^4*c^4 - a^4*b^4, z, 4)^2)/(2*b^2*c)

y =

root(2*a^2*b^2*z^4 - b^4*z^4 - a^4*z^4 - 4*a^2*b^2*d*z^3 + 4*b^4*d*z^3 - 2*a^2*b^2*l^2*z^2 + 2*a^2*b^2*d^2*z^2 - 2*a^2*b^2*c^2*z^2 + 2*b^4*l^2*z^2 - 6*b^4*d^2*z^2 - 2*b^4*c^2*z^2 + 2*a^4*b^2*z^2 - 2*a^2*b^4*z^2 - 4*b^4*d*l^2*z + 4*b^4*c^2*d*z + 4*a^2*b^4*d*z + 4*b^4*d^3*z + 2*b^4*d^2*l^2 + 2*b^4*c^2*l^2 + 2*a^2*b^4*l^2 - 2*b^4*c^2*d^2 - 2*a^2*b^4*d^2 + 2*a^2*b^4*c^2 - b^4*l^4 - b^4*d^4 - b^4*c^4 - a^4*b^4, z, 1)