I want to solve a simple equation
$Assumptions = 0 < v < 1 && x ∈ Reals && v ∈ Reals;
eqn1 = v == 1 - (1 - x)^(3/2)
sol = Solve[eqn1, {x},Reals]
But if I do a few more steps by hand
eqn2 = (1 - v)^(2/3) == ((1 - x)^(3/2))^(2/3) // PowerExpand
mySol = Solve[eqn2, {x}]
Did I miss some assumptions or something else? The assumtions from above don't seem to affect Solve
, only the domain parameter.
I know that this is not a proof!
Plot[{x /. mySol, x /. sol}, {v, 0, 1}, PlotStyle -> {Line, Dashed}]
v
? Mathematica assumes every variable is complex unless told otherwise. $\endgroup$ – J. M.'s ennui♦ Jan 20 '17 at 15:42Solve[eqn1, x, Reals] // ToRadicals // First
? $\endgroup$ – zhk Jan 20 '17 at 16:10