Given an expression like
a + b*y + c*y^2 + d*Sqrt[f + g*y + h*y^2]
How can I programatically, expand this to a quartic without any fractional powers?
Right now, I am having to copy and paste it as input expression and manually move the Sqrt to the RHS and square. I suspect there's an easier way to do this in Mathematica, perhaps using the Coefficient function or something similar.
A+B*y+C*y^2+D*Sqrt[F+G*y+H*y^2]==0
to the equation(A+B*y+C*y^2)^2 == D^2 (F+G*y + H*y^2)
. And you are fine with the fact that this may introduce extraneous roots (if your variables are real andSqrt[]
is interpreted as the positive square root). $\endgroup$Reduce[a + b*y + c*y^2 + d*Sqrt[f + g*y + h*y^2] == 0, y]
? This works better (gives shorter solutions) when you specify additional information about your coefficients. What's the underlying problem that you want to solve? $\endgroup$