*Problem:*

Let such that and . Find the minimum and the maximum value of the expression

.

*Solution:*

From the Cauchy – Schwarz Inequality we have that

,

or due to the hypothesis

.

From this last Inequality, we acquire

,

Let us now divide with . Then we get that

.

Solving this Inequality, gives us

.

Thus, and , *Q.E.D.*

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