要如何求代数式1/x+2/(1-x)的最大值与最小值,要如何求出值域呢？

Question

要如何求代数式 1/x + 2/(1-x) 的最大值与最小值,
要如何求出值域呢？

Answer 1

x≠0;1y=(1-x +2x)/x(1-x)=(x+1)/(x-x^2) =>y(x-x^2)=x+1=>-yx^2+yx-x-1=0 =>yx^2-(y-1)x+1=0; x实数=>判别式 [-(y-1)]^2 - 4y≥0 => y^2-6y +1≥0=>y^2-6y≥-1=>y^2-6y+9≥8 =>(y-3)^2≥8 =>|y-3|≥2√2 => y-3≥2...