2. 外语
  3. If x, y, and z are positive integers and x2=y2+z2, which of the following must be true?Ⅰ.x＞z Ⅱ.x=y+z Ⅲ. y2+z2 is a positive inte

If x, y, and z are positive integers and x2=y2+z2, which of the following must be true?Ⅰ.x＞z Ⅱ.x=y+z Ⅲ. y2+z2 is a positive inte

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问题 If x, y, and z are positive integers and x2=y2+z2, which of the following must be true?Ⅰ.x＞z Ⅱ.x=y+z Ⅲ. y2+z2 is a positive integer
选项 A、Ⅰ only
B、Ⅱ only
C、Ⅲ only
D、Ⅰ and Ⅱ only
E、Ⅰ and Ⅲ only
答案E
解析 Statement Ⅰ must be true, because if all three variables are positive integers and x2=z2 plus the square of another positive integer, then x has to be greater than z;, plug in numbers to verify. Ⅲ must be true because the square of a positive integer is always a positive integer, and y2+z2 is equal to the square of a positive integer (i.e.=x2). Ⅱ does not have to be true because if you square both sides of x=y+z, you get x2=y2+2yz+z2, which does not agree with the original statement.
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