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:因為a,b 都是整數(shù),所以a-2b 8-a也是整數(shù),
因為1只能分解為1×1或(-1)×(-1),
所以①a-2b=1,8-a=1,此時a=7,b=3;
②a-2b=-1,8-a=-1,此時a=9,b=5;
因此a+b=10或a+b=14.
故答案為10或14.
點評:解答此題的關(guān)鍵抓住整數(shù)的性質(zhì),再把1分解為兩個整數(shù)的乘積,進(jìn)一步分析解決問題.
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