x,y,z都>0.且x+y+z=1.求证1/x+4/x+9/z>=36

Question

x,y,z都>0.且x+y+z=1.求证1/x+4/x+9/z>=36

Answer 1

解原式＝1／x＋4／y＋9／z＝（1／x＋4／y＋9／z）（x+y+z）=14+y／x＋4x／y＋9x／z＋y／x+9y／z+4z／y＞＝14+4+6+12=36