if a is an algebraic number satisfying a^3+a+1 = 0 and b is an algebraic number satisfying b^2+b-3 = 0 prove that both a+b and ab are algebraic
The Attempt at a Solution
a is root of equation x^3+x+1 = 0 and similarly b, so there exists a x = ab,and also x = a+b. so, ( x- ab)(x - a+b) is the required one.
Its from I N Herstein's Topics in Algebra 5.1.13