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## Homework Statement

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

## Homework Equations

## 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

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