Both questions are similar in that the their root's relation to the previous roots are the same and so using a substitution may be easier. For example in question 2 we have which has roots and . Find the quadratic equation with roots and . Since the relation to the previous roots are the same we can define (Note is the root of the first equation and is the root of the equation we are required to find) . This implies that . Subbing this into the first equation gives and thus, is the required equation.
In the first example a similar technique can be used except we define
Now you started off right with the technique you chose in question 2. I think the reason you think it is wrong is because you get 6 and this isn't the middle term...... However you have not followed through. If you had you would notice you are right. We have . As you have already stated.....
Now the for the new equation we have,
So following on from that, . Thus our equation is .
Hope this helps.