Question

Can this problem be done like this
@ganeshie8

Answer 1

Find the greatest value of xyz for positive value of x,y,z subject to the condition
xy+yz+zx =12

Answer 2

This is the problem

Answer 3

Looks like Lagrange Multipliers.

Answer 4

Again GM and AM coming to rescue probably

\[\huge \frac{ xy+yz+zx }{ 3 } \ge (x ^{2}y ^{2}z ^{2})^{1/3}\]