Question

if a+b=1+ab then prove that a³+b³=1+a³b³​

Answer 1

Answer:

Given a/b + b/a = 1

(a^2 + b^2)/ab = 1.

a^2 + b^2 = ab --- (1)

Then a^3 + b^3 = (a + b)(a^2 + b^2 - ab)

= (a + b)(ab - ab) (From (1))

= 0.