The equation
-sqrt(k x) = sqrt(k x)
is solved correctly by Maple:
solve(-sqrt(k*x) = sqrt(k*x));
{k = k, x = 0}, {k = 0, x = x}
However, the equation
-sqrt(k x) = sqrt(k x + k - 1)
is apparently not solved correctly:
solve(-sqrt(k*x) = sqrt(k*x+k-1));
{k = 1, x = x}
The variable
x
can not be arbitrary since this equation reduces to the former equation
-sqrt(k*x) = sqrt(k*x);
when k = 1
.
Maple should return something similar to (4) below.
eval(-sqrt(k*x), k = 1) = eval(sqrt(k*x+k-1), k = 1);
(1/2) (1/2)
-x = x
solve({-x^(1/2) = x^(1/2)});
{x = 0}
Can this be explained in some way, or is this a bug?