Let α and β be two numbers where α

Question

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

MARKS Content Team · Accepted Answer

Correct answer: 48. Given, α and β be two number where α<β . ∵ The geometric mean of these numbers exceeds the smaller number α by 12 . i.e. √(αβ)=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

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

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