Question

已知x＞0y＞0z＞0,且x+y+z=1 求证1/x+4/y+9/z≥36

Answer 1

已知x>0y>0z>0,且x+y+z=1求证1x+4y+9z>=36

1 / x + 4 / y + 9 / z = (x+y+z) / x + 4 (x+y+z) / y + 9 (x+y+z) / z = 1 + y / x + z / x + 4 x / y +4 + 4 z / y + 9 x / z + 9 y / z + 9 = 1 + 4 + 9 + ( y / x + 4 x / y ) + ( z / x + 9 x / z ) + ( 4 z / y + 9 y / z ) >= 36