Question

If p+q = - 2, show that p^3 + q^3 +8 =6pq

Answer 1

Explanation:

Algebraic Identities:

Identity used: (a +b)³ = a³ + b³ + 3ab(a +b)

p + q = -2 ------------------(I)

Both sides take cube,

(p +q)³ = (-2)³

a = p and b =q

p³ + q³ + 3pq(p +q) = -8

p³ + q³ + 3pq*(-2) = - 8 {From (I)}

p³ + q³ - 6pq = -8

p³ + q³ = -8 + 6pq

p³ + q³ + 8 = 6pq

Hence, proved.