第二届北方数学奥林匹克邀请赛第5题为:已知正数a、b、c满足a+b+c=3,求证:(a~2+-)/(2a~2+(b+c)~2)+(b~2+9)/(2b~2+(c+a)~2)+(c~2+9)/(2c~2+(a+b)~2)≤5.本文先给出它的推广:已知正数x_1、x_2、…、x_n满足x_1+x_2+…+x_n=n.求证:(x_1~2+n~2)/((n-1)x_1~2+(sum from i=1 to n x_i-x_1)~2)+ The 5th title of the 2nd North Mathematical Olympiad Invitational is: Known positive numbers a, b, and c satisfy a+b+c=3. Proof: (a~2+-)/(2a~2+(b+c)~ 2) +(b~2+9)/(2b~2+(c+a)~2)+(c~2+9)/(2c~2+(a+b)~2)≤5. First give its generalization: Known positive numbers x_1, x_2, ..., x_n satisfy x_1+x_2+...+x_n=n. Proof: (x_1~2+n~2)/((n-1)x_1~2+( Sum from i=1 to n x_i-x_1)~2)+