Question

求函数的最小值

X^2+2X/X^2+2最小值怎么算？麻烦说详细一点，谢谢有加分的

Answer 1

X^2+2X/X^2+2最小值是在X<0的区间取得
(X^2+2X)/(X^2+2)=1+(2X-2)/(X^2-1+3)=1+2/{X+1+[3/(X-1)]}
=1+2/{X-1+[3/(X-1)]+2}
在X<0的区间，X-1+[3/(X-1)]的最大值=-2√3 此时X=1-√3
(X^2+2X)/(X^2+2)最小值=1+2/(-2√3+2)=(1-√3)/2

Answer 2

-127

Answer 3

原式=x^2+2x/(x^2+2)+1/(x^2+2)^2-1/(x^2+2)^2=[x+1/(x^2+2)]^2-1/(x^2+2)^2=x[x+2/(x^2+2)]当x=0时值最小。最小是0

Answer 4

X^2+2X/X^2+2最小值是在X<0的区间取得
(X^2+2X)/(X^2+2)=1+(2X-2)/(X^2-1+3)=1+2/{X+1+[3/(X-1)]}
=1+2/{X-1+[3/(X-1)]+2}
在X<0的区间，X-1+[3/(X-1)]的最大值=-2√3 此时X=1-√3原式=x^2+2x/(x^2+2)+1/(x^2+2)^2-1/(x^2+2)^2=[x+1/(x^2+2)]^2-1/(x^2
(X^2+2X)/(X^2+2)最小值=1+2/(-2√3+2)=(1-√3)/2