If a + b = p, ab = q, then (a 4+ b 4) is equal to

Explanation

Given: a + b = p, ab = q Formula: (a + b) 2= a 2+ b 2+ 2ab Calculation: (a + b) 2= a 2+ b 2+ 2ab p 2= (a 2+ b 2) + 2q (a 2+ b 2) = p 2- 2q Then, (a 4+ b 4) = (a 2+ b 2) 2- 2a 2b 2 = (p 2- 2q) 2- 2q 2 = p 4- 4p 2q + 2q 2 ∴ (a 4+ b 4) = p 4- 4p 2q + 2q 2