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If A and B are the H.C.F. and L.C.M. respectively of two algebraic expressions p and q, and A + B = p + q, then the value of A3 + B3 is
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- p3 – q3
- p3
- q3
- p3 + q3
Correct Option: D
Let the numbers are p and q and HCF = A, LCM = B
Using Rule, we have
Product of numbers = HCF × LCM
pq = AB
⇒ p + q = A + B (given) ...(i)
(p – q)2 = (p + q)2 – 4pq
or, (p – q)2 = (A + B)2 – 4AB
or, (p – q)2 = (A – B)2
or, (p – q) = A – B ...(ii)
Using (i) and (ii), we get
p = A and q = B
∴ A3 + B3
= p3 + q3
