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Let x and y be nonnegative real numbers. If xy = \frac{2}{5}, then find the minimum value of 6x + \frac{3}{5y}.

 May 27, 2024
 #1
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First, let's isolate y in the first equation. 

 

\(xy = 2/5 \\ y = 2 / (5x) \)

 

Plugging this value into the second expression, we get 

\(6x + 3 / (2 / (5x) ) = \\ 6x + (15/2)x = \\ (27/2) x\)

 

However, notice that there is no mimumum value or maximum value because the smaller x is, the smaller the number is to no limit. 

 

There are absolutely no restrictions for this expression. 

 

Thanks! :)

 May 27, 2024

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