Funny thing is the 4u students get taught an easier method... namely:
y=f(x), solve for x, then substitute x into the equation you're trying to solve... where f(x) equals something the roots have changed to, e.g. all the roots have squared, or inverted, or inverted AND squared.
If you wanted the equation with roots a^2, b^2, y^2, you'd go: y=x^2 -> sqrty=x, then substitute sqrty every time you see x in the original equation... then manipulate to get an equation in integral powers of y... which can be tricky... it involves squaring both sides, usually.