Question

不等式最大值最小值 已知x>-1求x取何值时,x+4/x+1的最小值

Answer 1

最讨厌提问者写式子时不加括号
＝＝＝＝＝＝
x+[4/(x+1)]
=(x+1)+[4/(x+1)]-1
≥2√[(x+1)*4/(x+1)]-1
=2√4-1
=3
当x+1=4/(x+1),(x+1)²=4,x=1时,不等式取等号
即当x=1时,式子x+[4/(x+1)]取最小值3