解一个二元四次的方程组：Solve[{0.5*x^4/(0.5^4 + x^4) + 1*0.5^4/(0.5^4 + y^4) - x == 0,
0.5*y^4/(0.5^4 + y^4) + 1*0.5^4/(0.5^4 + x^4) - y == 0}, {x,
y}, Reals]
解的实数解：{{x -> 0.0123965, y -> 1.4938}, {x -> 0.637354, y -> 0.637354}, {x -> 1.4938, y -> 0.0123965}}
最初的方程：
Solve[{a*x^4/(0.5^4 + x^4) + 1*b^4/(0.5^4 + y^4) - x == 0,
a*y^4/(0.5^4 + y^4) + b*0.5^4/(0.5^4 + x^4) - y == 0}, {x,
y}, Reals]
a，b是这个方程的系数，是可以变得。可以得到不同个数的解 我现在的难题是a，b变化时，比如都从0-1时这么时候解的个数我怎么统计 真心求教 急。。。。。。。。

Solve[{a*x^4/(0.5^4 + x^4) + b*0.5^4/(0.5^4 + y^4) - x == 0,
a*y^4/(0.5^4 + y^4) + b*0.5^4/(0.5^4 + x^4) - y == 0}, {x,
y}, Reals]
原方程是这样

这样用Solve结果可能不准,
暂时想到暴力求解
dd = .05;
sol = ParallelTable[{a, b,
Solve[{a*x^4/(0.5^4 + x^4) + b*0.5^4/(0.5^4 + y^4) - x == 0,
a*y^4/(0.5^4 + y^4) + b*0.5^4/(0.5^4 + x^4) - y == 0}, {x, y},
Reals] // Quiet // Length}, {a, 0, 1, dd}, {b, 0, 1, dd}];
ListContourPlot[sol~Flatten~1]
或者
ContourPlot[
Solve[{a*x^4/(0.5^4 + x^4) + b*0.5^4/(0.5^4 + y^4) - x == 0,
a*y^4/(0.5^4 + y^4) + b*0.5^4/(0.5^4 + x^4) - y == 0}, {x, y},
Reals] // Quiet // Length, {a, 0, 1}, {b, 0, 1}, PlotPoints -> 2,
MaxRecursion -> 4, Mesh -> All, PlotLegends -> Automatic]