If $x > 0, y > 0$ and $x y = 25$ , then find the minimum value of $x + y$ .

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Solution

We have,
$\begin{matrix} x y = 25 d i f f e r e n t i a t e w . r . t o x p u t \Rightarrow y = \frac{25}{x} t h e n, min i m u m v a l u e o f (x + y) \Rightarrow x + y = \Rightarrow x + \frac{25}{x} \Rightarrow a - \frac{25}{x^{2}} = 0, x = 5 h e n c e, min i m u m v a l u e o f (x + y) = 10 \end{matrix}$

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