1.If x is an integer greater than 1 and if y = x + 1/x,which of the following must be true?

题目

1.If x is an integer greater than 1 and if y = x + 1/x,which of the following must be true?
I.y x II.y is an integer.III.xy > x^2
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I,II,and III

答案

列表
x y
2 2+1/2
3 3+1/3
4 4+1/4
5 5+1/5
6 6+1/6
y =!x
套2 !2=2*1=2
套3 !3=3*2*1=6
因此 I项排除
y is an integer(整数),从上表可知y不可能是整数
xy > x^2
2*5/2 = 5 > 2*2=4
3*10/3 =10 > 3*3=9
因此III 是对的
答案是 (B) III only