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I need help on this

 

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

 Dec 19, 2023
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By AM-GM, we have [x + \frac{1}{y} \ge 2 \sqrt{x \cdot \frac{1}{y}} = 2 \sqrt{\frac{1}{5}} = \frac{2 \sqrt{5}}{5}.]

 

Therefore, 6x+5y3​≥6(x+y1​)−59​=5125​​−59​=535​−9​​.

 

Equality occurs when x=y1​=5​1​, so the minimum value is actually attained.

 Dec 19, 2023

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