If (a, b, c, d) are positive real numbers such that (a + b +... | Mathematics | SolveeIt

Question

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.

$0 < M \le 1$

$1 < M \le 2$

$2 \le\, M \le 3$

$3 \le\, M \le 4$

Answer

$0 < M \le 1$

Explanation

Solution

Since, $AM \ge GM$ , then
$\hspace15mm \frac{(a + b) + (c + d)}{2} \ge \sqrt {(a+ b)\, (c+d)} \Rightarrow M \le 1$
Also, $\hspace5mm (a + b) + (c +d) > 0 \hspace15mm [\because a, b, c, d > 0]$
$\therefore \hspace30mm 0 < M \le 1$

Mathematics Question on Sequence and series

Solution