Let α and β be two numbers where α < β . The geometric mean of these numbers exceeds the smaller number α by 12 and the arithmetic mean of the same numbers is smaller by 24 than the larger number β , then the value of | β - α | is

Step-by-step solution

Given, α a n d β be two number where α < β . ∵ The geometric mean of these numbers exceeds the smaller number α by 12 . i.e. α β = α + 12 .....(i) And the arithmetic mean of the same numbers is smaller by 24 than the number β . i.e. α + β 2 = β - 24 ......(ii) By solving Equations. (i) and (ii), we get α = 6 , β = 54 ∴ β - α = 54 - 6 = 48