Question

If `y z+z x+x y=12 ,w h e r ex ,y ,z` are positive values, find the greatest value of `x y zdot`

Answer 1

Using A.M `ge` G.M we have
`(xy + yz + zx)/(3) ge (x^(2) y^(2) z^(2))^(1//3)`
`implies (x)/(3) ge (x^(2) y^(2) z^(2))^(1//2)`
`implies (xyz)_("max") = ((12)/(3))^(3//2)`