Follow the idea of the next exercise or you may want to start with writing
For a while choose . Same for . Then
By first, squaring both sides you will earn a monic relation for but it has (only) one sqrt so after squaring it for second time you will have a monic relation with no sqrt at . If then everything is finished without needing computing the exact relations but if you simplify it, no coefficient will have . The same method will work for but I have doubt if the second method give us a better monic relation than a relation at , you may want to compute it to see. After making first square you will have;
Now we go for the second squaring, but as we want to get rid of radicals we take to the left hand side and then we square sides.
It's obvious that all coefficients will be in and won't have and we only need to pay attention to the constant coefficient.
Now one can see the simplified form and for sure there is no fractions like or . "For we will encounter 3 radicals! What can we do?" Don't be afraid! 3 radicals is not a very scay case yet. For getting rid of 3 radicals in an equation like do as following;
Take a square
Then we are in case with two radicals;
Now let's be sure that we won't have coefficients with and so on.