若x,y属于R+,则不等式1/x+1/y+k/(x+y)≥0恒成立的实数k取值范围是
问题描述:
若x,y属于R+,则不等式1/x+1/y+k/(x+y)≥0恒成立的实数k取值范围是
答
移项,有1/x+1/y≥-k/(x+y)
即(x+y)/(xy)≥-k/(x+y)
即(x+y)^2/(xy)≥-k
又有(x+y)^2/(xy)≥4恒成立
所以为满足条件得k≥-4