Let - and - be two numbers where - - - The geometric mean of these numbers exceeds the smaller number - by 12 and the arithmetic mean of the same numbers is smaller by 24 than the larger number - Then the value of - - - is

√(αβ) = α + 12 ; α + β2 = β 24 ⇒β = α + 48 ∴α(α + 48) = nbsp;(α + 12)^2 ⇒α = 6 ⇒β = 54 ∴β α = 48 ...

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Standard XII

Mathematics

Geometric Mean

Let α and β b...

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

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Solution

The correct option is B $48$
$\sqrt{α β} = α + 12;$
$\frac{α + β}{2} = β - 24 \Rightarrow β = α + 48$
$∴ α (α + 48) = (α + 12)^{2}$
$\Rightarrow α = 6$
$\Rightarrow β = 54$
$∴ β - α = 48$

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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

The correct option is B 48√αβ=α+12; α+β2=β−24⇒β=α+48 ∴α(α+48)=(α+12)2 ⇒α=6 ⇒β=54 ∴β−α=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

The correct option is B $48$
$\sqrt{α β} = α + 12;$
$\frac{α + β}{2} = β - 24 \Rightarrow β = α + 48$
$∴ α (α + 48) = (α + 12)^{2}$
$\Rightarrow α = 6$
$\Rightarrow β = 54$
$∴ β - α = 48$