Find the maximum p such that 2x^4y^2 + 9y^4z^2 + 12z^4x^2 - px^2y^2z^2 is always nonnegative for all real x,y, and z .
Find the maximum p such that 2x4y2 + 9y4z2 + 12z4x2 - px2y2z2>0 for all real x,y,z . 2x4y2+9y4z2+12z4x2-px2y2z2=0
p(x2y2z2)=x2y2(2x2)+y2z2(9y2)+x2z2(12z2)
p=(2x2/z2)+(9y2/x2)+(12z2/y2), which is the maximum, for all real x,y,z
