Q97
ArithmeticNumber System, LCM/HCF & Divisibility
The H.C.F. of two natural numbers $a$ and $b$ is $h$ and their L.C.M. is $L$, then value of $a^2 + b^2$ is (Given $h + L = a + b$)
- a.$h^3 + L^3$
- b.$h + L$
- c.$h^2 + L^2$
- d.$h^3 - L^3$
Answer: (C) $h^2 + L^2$
For two numbers, $ab = hL$, and here $a + b = h + L$. So $a^2 + b^2 = (a + b)^2 - 2ab = (h + L)^2 - 2hL = h^2 + L^2$. Option B is $a + b$ itself, not the sum of squares.