Question

If p+q=1+pq, then prove that p^3+q^3=1+p^3q^3

Answer 1

Step-by-step explanation:

p3 + q3 = (p + q)(p2 + q2 - pq)

so, p3 +q3

= (1 + pq)((p + q)^2 - 2pq -pq)

= (1 +pq)(1 + p2q2 + 2pq -2pq - pq)

= (1 +pq)(1 +p2q2 - pq)

= (1 + p3q3)

:)