设实数xy满足x+y-3≤0,y-x/2≥0,x-1≥0,则求u=y/x-x/y的取值范围
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![设实数xy满足x+y-3≤0,y-x/2≥0,x-1≥0,则求u=y/x-x/y的取值范围](/uploads/image/z/1614949-61-9.jpg?t=%E8%AE%BE%E5%AE%9E%E6%95%B0xy%E6%BB%A1%E8%B6%B3x%2By-3%E2%89%A40%2Cy-x%2F2%E2%89%A50%2Cx-1%E2%89%A50%2C%E5%88%99%E6%B1%82u%3Dy%2Fx-x%2Fy%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
设实数xy满足x+y-3≤0,y-x/2≥0,x-1≥0,则求u=y/x-x/y的取值范围
设实数xy满足x+y-3≤0,y-x/2≥0,x-1≥0,则求u=y/x-x/y的取值范围
设实数xy满足x+y-3≤0,y-x/2≥0,x-1≥0,则求u=y/x-x/y的取值范围
设实数xy满足x+y-3≤0,y-x/2≥0,x-1≥0,则求u=y/x-x/y的取值范围
x+y-3≤0.(1)
y-(x/2)≥0,.(2)
x-1≥0.(3)
化出三条直线:x+y-3=0;y-(x/2)=0;x-1=0;三条直线的交点意次为A(1,2);B(1,1/2);
C(2,1);动点(x,y)就在以这三点为顶点的△ABC内(含边界).
不难看出:1/2≤y/x≤2,2≥y/x≥1/2;
两式相减即得 -3/2≤y/x-x/y≤3/2.
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