Question

比较x^2+1/x^2+1与1的大小,并指出等号成立条件

Answer 1

x^2+1/(x^2+1)-1=(x^2+1)+1/(x^2+1)-2=[根号(x^2+1)+根号1/(x^2+1)]^2>=0

所以x^2+1/(x^2+1)>=1

如果x^2+1/(x^2+1)=1

x^2+1=1/(x^2+1)

x^2+1=1

x=0