Question

求函数y=x方除以x-1的最小值(x>1)

Answer 1

y=x方除以x-1

=(x^2-1)/(x-1)+1/(x-1)
=(x+1)+1/(x-1)
=(x-1)+1/(x-1)+2

≥4
当且仅当(x-1)=1/(x-1)时等号成立
此时x=2

Answer 2

x>1
x-1>0

y=(x²-1+1)/(x-1)
=(x²-1)/(x-1)+1/(x-1)
=x+1+1/(x-1)
=(x-1)+1/(x-1)+2≥2√[(x-1)*1/(x-1)]+2=4
所以最小值是4