Question

当x变化时,求分式(3x*x+6x+5)/(1/2x*x+x+1)的最小值

Answer 1

(3x*x+6x+5)/(1/2x*x+x+1)=6[(x+1)^2+2/3]/[(x+1)^2+1]=6{1-1/3/[(x+1)^2+1]}
x=-1时原式有最小值

Answer 2

(3X^+6X+5)/(0.5X^+X+1)
=6- 1/(0.5X^+X+1)
=6- 2/(X^+2X+2)
=6- 2/[(X+1)^+1]
∵(X+1)^+1≥1
∴2/[(X+1)^+1]小于等于2
∴分式最小值为4.