1. Tardigrade
  2. Question
  3. Mathematics
  4. If a, b, c, d are positive real numbers such that a + b +c + d = 2, then M =(a + b) (c+d) satisfies the relation.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $a, b, c, d$ are positive real numbers such that $a + b +c + d = 2,$ then $M =(a + b) (c+d) $ satisfies the relation.

IIT JEEIIT JEE 2000Sequences and Series

Solution:

Since, $ AM \ge GM$, then
$ \frac{(a + b) + (c + d)}{2} \ge \sqrt {(a+ b)\, (c+d)} \Rightarrow M \le 1 $
Also, $ (a + b) + (c +d) > 0 [\because a, b, c, d > 0]$
$ \therefore 0 < M \le 1 $