Let x,y, and z be nonnegative real numbers such that x+y+z=5. Find the maximum value of 2x+1+2y+1+2z+1.
Solution — click to reveal
By QM-AM, 3(2x+1)+(2y+1)+(2z+1)≥32x+1+2y+1+2z+1.Hence, 2x+1+2y+1+2z+1≤3(2x+2y+2z+3)=39.Equality occurs when x=y=z=35, so the maximum value is 39.