Question

已知实数x>0,y小于等于1且满足xy+2x+y-2=0

Answer 1

实数x>0,y小于等于1

xy+2x+y-2=0

(x+1)*y=2-2x

y=2(1-x)/(x+1)

因y≤1

得 2(1-x)/(x+1)≤1

(2-2x-x-1)/(x+1)≤0

(3x-1)/(x+1)≥0

又知x>0 x+1>0

所以3x-1≥0

x的取值范围x≥1/3

z=2x+y=2x+2(1-x)/(x+1)=2x-2+4/(x+1)

=2(x+1)+4/(x+1)-4

≥2√[2(x+1)*4/(x+1)]-4

=4√2-4

可见你的答案正确