Which of the following inequalities is always true for any two positive real numbers and ?

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Which of the following inequalities is always true for any two positive real numbers

x

and

y

? (a)

\dfrac{x+y}{2} \le \sqrt{xy}

(b)

\dfrac{x+y}{2} \ge xy

(c)

\dfrac{x+y}{2} \ge \sqrt{xy}

(d)

\dfrac{x-y}{2} \ge \sqrt{xy}