下面的问题具有一定的普遍性，带着假设的方程往往求解会出现空解或者是漏解警告，不能提供更多的信息，大佬acer 提供了一个有益的尝试的解法，主要是利用化简命令的参数化选项进行求解，很值得去体会。

问题描述：Why won't Maple solve any of these inequalities for Q?

At first I tried solving the system of equations, but then I tried solving the inequalities individually for Q, and those too could not be solved by Maple. What am I doing wrong?

restart;

assume(R1, real, R2, real, RL, real, XC1, real, XC2, real, XL1, real);;

additionally(0 < R1, 0 < R2, 0 < RL, 0 < XC1, 0 < XC2, 0 < XL1);

eq3 := 0 < R1*(4*Q^2 + 1) - RL;

eq4 := 0 <= 4*Q^2*R1*RL - (R1 - RL)^2;

eq5 := 0 < Rs^2*(RL - R1)/Q^2 + R1^2*RL

sys1 := {eq3, eq4, eq5};

{solve}(sys1, {Q}) assuming (RL < R1);

{solve}(sys1, {Q}) assuming (R1 < RL);

solve(sys1,{Q});Warning, solutions may have been lost

solve(eq3, Q);Warning, solutions may have been lost

solve(eq4, Q);#Warning, solutions may have been lost

solve(eq5, Q);#Warning, solutions may have been lost

2 解决参考方案

restart;

kernelopts(version);

interface(showassumed = 0);

eq3 := 0 < R1*(4*Q^2 + 1) - RL;

eq4 := 0 <= 4*Q^2*R1*RL - (R1 - RL)^2;

eq5 := 0 < Rs^2*(RL - R1)/Q^2 + R1^2*RL;

sys1 := {eq3, eq4, eq5};This variant contains only three branches, which is interesting.

note: don't reexecute this line after applyting the additionally clauses below.

simplify(solve(sys1, {Q}, parametric)) assuming (Rs::real, 0 < R1, 0 < R2, 0 < RL, RL < R1)This invocation (without the assuming, contains the restrictions on R1,RL in the conditions of the output. You may prefer not to see that. Hence providing the assumptions may serve you some purpose (even if only under the simplify step).

note: don't reexecute this after applying the additionally calls further on.

simplify(solve(sys1 union {0 < R1, 0 < R2, 0 < RL, RL < R1}, {Q}, parametric)) assuming Rs::real

additionally(R1, real, R2, real, RL, real, XC1, real, XC2, real, XL1, real);

additionally(0 < R1, 0 < R2, 0 < RL, 0 < XC1, 0 < XC2, 0 < XL1);

simplify(solve(sys1, {Q}, parametric)) assuming (RL < R1);

simplify(solve(sys1, {Q}, parametric)) assuming (Rs::real, RL < R1)

本文源自https://www.mapleprimes.com/questions/230985-Solving-Inequalities​www.mapleprimes.com