x,y∈(0,1),x≠y.xy=1/16,m=log(1/4)x*log(1/4)y,求m的取值范围高二数学

Question

x,y∈(0,1),x≠y.xy=1/16,m=log(1/4)x*log(1/4)y,求m的取值范围
高二数学

Answer 1

log(1/4)X+log(1/4)Y>=2根号(log(1/4)x*log(1/4)y)
log(1/4)X+log(1/4)Y>=2根号M
log(1/4)X+log(1/4)Y=log(1/4)XY=log(1/4)1/16=2
2>=2根号M
根号M