Question

已知x>2,f(x)=x2-3x+5/x-2,则f(x)有最___值,为___此时x的值为___

Answer 1

f(x)=(x²-3x+5)/(x-2)

=(x²-2x-x+2+3)/(x-2)

=[x(x-2)-(x-2)+3]/(x-2)

=x -1 +3/(x-2)

=(x-2) +3/(x-2) +1

x>2,x-2>0,由均值不等式得,当x-2=3/(x-2)时,即x=2+√3时,

(x-2)+3/(x-2)有最小值2√3,此时f(x)有最小值2√3+1.

已知x>2,f(x)=x2-3x+5/x-2,则f(x)有最( 小 )值,为( 2√3+1 ),此时x的值为( 2+√3 ).