Given that p - 1- What is the minimum value of p 2-625- p 2 -A- 5B- 10C- 25D- 50

The correct option is D 50 The minimum value will occur when p^2=625/p^2 p^4=625 ⇒ p=5 Putting the value of p in the equation, min value =p^4=625 ⇒ p=5 ⇒ =25+ ...

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Standard XII

Mathematics

Sufficient Condition for an Extrema

Given that p ...

Question

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

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Solution

The correct option is D
50

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

The correct option is D 50 The minimum value will occur when p2=625p2 p4=625⇒p=5 Putting the value of p in the equation, min value =p4=625⇒p=5⇒=25+62525=25+25=50

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

The correct option is D
50

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 = $p^{4} = 625 \Rightarrow p = 5 \Rightarrow= 25 + \frac{625}{25} = 25 + 25 = 50$