If we are given that x+x1=a, then we know that x2+x21=a2−2 and x3+x31=a3−3a. However, it's not too clear how we can relate the latter 2 equations with each other.
Let x be a real number such that x3+x31=102, what is the value of x2+x21?
Your answer seems reasonable.
Find out if you're right!