How to solve

x sqrt(1+x) + sqrt(3-x) = 2 sqrt(x^2+1) ?

First, square both sides of the equation. That gets rid of the radical on the right and leaves you with just one radical on the left, along with some terms outside of the radical. Then combine all of the terms outside of the radical on one side of the equation, leaving the one square root term on the other side of the equation. Next, square both sides again. That will eliminate the radical on one side, and leave a 6th-order polynomial on the other. Finally, combine all terms on one side of the equation, and find the roots of the resulting 6th-order polynomial.