if a and b are both positive intergers and a平方-b平方=7 .what is the value of a

题目

if a and b are both positive intergers and a平方-b平方=7 .what is the value of a

答案

　　原句翻译为：如果a和b都是正整数,且a²-b²=7,那么a的值是多少?
由题意,可得：
a²-b²=7
即（a+b）（a-b）=7
∴a+b=7,a-b=1
或a+b=-7,a-b=-1
解得：a=4或-4,b=3或-3
又∵a,b＞0
∴a=4,b=3
　　答：a的值为4.