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1/(1 + x^(-2)) = 1/2 is answered with the empty set, though x = 1 and x = -1 are roots #2144
Description
An equation with a negative power is answered with the empty set, which claims there is no root:
| Input | Answer | Should be |
|---|---|---|
solve::x::1/(1+x^(-2)) = 1/2 |
{ } |
{ 1, -1 } |
solve::p::1/(2+p^(-3)) = 1/3 |
{ } |
{ 1, … }, the cube roots of 1 |
The same equations written another way are solved:
1/(1+1/x^2) = 1/2gives{ 1, -1 }.x^(-2) + 1 = 2gives{ 1, -1 }.- With a first power,
1/(1+x^(-1)) = 1/2gives{ 1 }.
An empty answer is a claim that there is no solution. Where the solver cannot invert, it should leave the equation unsolved.
Found while reading Modenov's Problems in Geometry for #2131.
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