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NDA 2021

Exam: NDA
Year: 2021
Subject: Mathematics
Chapter: Quadratic Equation

NDA 2021 · Mathematics · Quadratic Equation

If x+y=20 and P=x y , then what is the maximum value of P ?

If

x+y=20

and

P=x y

, then what is the maximum value of

P

?

Options

A $100$
B $96$
C $84$
D $50$

Correct answer

A. $100$

Step-by-step solution

x+y=20 \text{ and } P=x y

A.M. of

x

and

y=\frac{x+y}{2}=\frac{20}{2}=10

. G.M. of

x

and

y=\sqrt{x \cdot y}=\sqrt{P}

As, A.M. \geq G.M.

\therefore 10 \geq \sqrt{P}

Hence,

P_{\max.}=(10)^2=100

.

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