Question

if x,y,z are positive real number then show that

Answer 1

$\sqrt{1/x*y*1/y*x*z*1/z}$
$\sqrt{1}$
=1

Answer 2

According to given sum,

$= > \: \sqrt{ {x }^{ - 1} y} \: \times \sqrt{ {y}^{ - 1} z} \: \times \sqrt{ {z}^{ - 1}x }$

$= > \: \sqrt{ \frac{x}{y} } \times \sqrt{ \frac{y}{z} } \: \times \sqrt{ \frac{z}{x} }$

$= > \: \sqrt{ \frac{x}{y} \times \frac{y}{z} \times \frac{z}{x} }$

$= > \: \sqrt{1}$

=> 1

LHS = RHS

:-)Hope it helps u.