当x分别为1/2005,1/2004,1/2003.1/2002.1/2001.1/2000.2000,2001,2002,200_数学解答

当x分别为1/2005,1/2004,1/2003.1/2002.1/2001.1/2000.2000,2001,2002,2003,2004,2005计算代数式x²/1+x²的值,将所得的结果相加,其和为____
我知道答案是=6.但能麻烦给个解答过程.吗?

人气：284 ℃　时间：2020-06-17 02:10:27

解答

令x1=2000,y1=1/x1则x1^2/(x1^2+1) +y1^2/(y1^2+1) =x1^2/(x1^2+1)+(1/x1)^2/((1/x1)^2+1)=x1^2/(x1^2+1)+1/(x1^2+1)=(x1^2+1)/(x1^2+1)=1所以2000+1/2000+2001+1/2001+2002+1/2002+2003+1/2003+2004+1/2004+2005+1/...