Suppose both a and b are  integer．As （a-2b）（8-a）=1，then a+b=
10
10
or
14
14
分析：由a，b都是整數(shù)，得出（a-2b）和（8-a）也是整數(shù)，而乘積為1，可以得出兩個(gè)因數(shù)同為1或-1，由此求得a、b的值，問題得以解決．
解答：解：因?yàn)閍，b 都是整數(shù)，所以a-2b 8-a也是整數(shù)，
因?yàn)?只能分解為1×1或（-1）×（-1），
所以①a-2b=1，8-a=1，此時(shí)a=7，b=3；
②a-2b=-1，8-a=-1，此時(shí)a=9，b=5；
因此a+b=10或a+b=14．
故答案為10或14．
點(diǎn)評(píng)：解答此題的關(guān)鍵抓住整數(shù)的性質(zhì)，再把1分解為兩個(gè)整數(shù)的乘積，進(jìn)一步分析解決問題．
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