设x>-1,求函数y=(x+5)(x+3)/(x+1)最小值

设x>-1,求函数y=(x+5)(x+3)/(x+1)最小值 .解 y=(x+5)(x+3)/(x+1)=6+[(x+1)+8/(x+1)]=6+4√2+[(x+1)-4√2+8/(x+1)]=6+4√2+[√(x+1)-2√2/√(x+1)]^2>=6+4√2,当x=2√2-1时,等号成立.因此,函数y=(x+5)(x+3)/(x+1)最小值是6+4√2.

设x＞-1,求函数y=(x+5)(x+3)/(x+1)最小值y = (x+5)(x+3)/(x+1) = (x+1+4)(x+1+2)/(x+1) = [(x+1)²+6(x+1)+8]/(x+1) = (x+1)+8/(x+1) + 6 .............x+1＞0 ≥2•√8 + 6--->x+1=8/(x+1)即x=2√2-1时，y有最小值4√2+6