Question

求涵数Y=X-1分之X的平方加8(X>1)的最小值

Answer 1

y=(x²+8)/(x-1)
=[(x-1)²+2(x-1)+9]/(x-1)
=(x-1)+9/(x-1)+2
x>1所以x-1>0
所以(x-1)+9/(x-1)>=2√(x-1)*[9/(x-1)]=6
所以y>=6+2=8
所以y最小值为8

Answer 2

y=(x^2+8)/(x-1)=[(x-1)^2+2(x-1)+9]/(x-1)
=(x-1)+9/(x-1)+2
>=2根号[(x-1)*9/(x-1)]+2,【因为x-1>0】
=2*3+2
=8
即最小值是8，当x-1=9/(x-1),即x=4时取得。