HCF and LCM of two numbers p and q is A and B respectively, if A + B = p + q, then the value of A3 + B3 is:
Answer & explanation
Correct answer: option 1
L.C.M × H.C.F = product of numbers
So, A × B = p × q ----(i)
And, it is given that A + B = p + q ----(ii)
we know,
A3 + B3 = (A + B)[(A + B)2 – 3AB]
⇒ A3 + B3 = p + q [(p + q)2 – 3pq]
∴ A3 + B3 = p3 + q3