Have you tried denoting x^2 + 1 by t?
(x²+2)/2=2√(x³+1)
Have tried a lot of things, but I am pretty certain that I am making a mistake in my initial steps so I dont think
a copy of my tries would be of help.
thanks in advance
First, that's not a polynomial equation. Second there is a missing "(" on the left. Is it supposed to be ?
And it is hard to read- that is on the right, not as emkarov seemed to think.
The first thing you should do is make it a polynomial equation by squaring both sides.
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By the "rational root theorem" the only possible roots of that are the factor of 12: 1, -1, 2, -2, 4, -4, 8, -8, 12, and -12.
And unless I have done the arithemtic wrong none of those satisfy the equation so the equation has only irrational or complex roots.