Given that p ≥ 1. What is the minimum value of p2+625p2?

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Given that p $\geq$ 1. What is the minimum value of $p^{2} + \frac{625}{p^{2}}$ ?

Options:

A . 5

B . 10

C . 25

D . 50

Answer: Option D
:
D

The minimum value will occur when $p^{2} = \frac{625}{p^{2}}$

$p^{4} = 625 \Rightarrow p = 5$

Putting the value of p in the equation, min value = $p^{4} = 625 \Rightarrow p = 5 \Rightarrow= 25 + \frac{625}{25} = 25 + 25 = 50$

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