已知x>1,求函数y=2+3x+4⼀(x-1)的最小值

2025-05-14 12:42:39
推荐回答(2个)
回答1:

x>1,
y=3(x-1)+4/(x-1)+5,
根据均值不等式,
3(x-1)+4/(x-1)>=2√[3(x-1)*4/(x-1)=4√3,
y(min)=4√3+5.

回答2:

y=5+3(x-1)+4/(x-1)≤5+2√(3(x-1)*4/(x-1))=5+4√3
当且仅当x=1+2√3/3