First slide

Means - A.M/G.M/H.M

Question

$If x, y, z are positive integers then value of expression (x + y) (y + z) (z + x) is:$

Moderate

A

$= 8 x y z$
B

$> 8 x y z$
C

$< 8 x y z$
D

$= 4 x y z$

Solution

$\begin{array}{l} A.M > G.M \\ \begin{aligned} \frac{x + y}{2} > \sqrt{x y} \\ \frac{y + z}{2} > \sqrt{y z} \\ \frac{z + x}{2} > \sqrt{z x} \\ \frac{(x + y) (y + z) (z + x)}{8} > x y z \\ Or \\ (x + y) (y + z) (z + x) > 8 x y z \end{aligned} \end{array}$

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