Y=(x平方-3x+3)除以x-2 (x大于2)的最小值
网友回答
x²-3x+3=(x-2)²+x-1=(x-2)²+(x-2)+1
y=(x²-3x+3)/(x-2)
=(x-2)+1+1/(x-2)
>=2√[(x-2)×1/(x-2)]+1 (当且仅当(x-2)=1/(x-2),即x=3时取等)
=3所以,y的最小值为3
======以下答案可供参考======
供参考答案1:
x²-3x+3=(x-2)²+x-1=(x-2)²+(x-2)+1
y=(x²-3x+3)/(x-2)
=(x-2)+1+1/(x-2)
>=2√[(x-2)×1/(x-2)]+1 (当且仅当(x-2)=1/(x-2),即x=3时取等)
=3,y的最小值为3