If H and L are the HCF and LCM respectively of two numbers x and y, and H + L = x + y, then value of H³ + L³ is?

x³ + y³

Here, HCF × LCM = x × y

⇒ H × L = x × y ..............(i)

and ATQ,

H + L = x + y       .............(ii)

Cubing both side, we get

⇒ H³ + L³ + 3HL (H + L) = x³ + y³ + 3xy (x + y)

⇒ H³ + L³ + 3xy (x + y) = x³ + y³ + 3xy (x + y)        [From (i) & (ii)]

⇒ H³ + L³ = x³ + y³