已知根号a加根号b=根号2009,且a大于b大于0,试求满足上式的整数对(a,b)的个数
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已知根号a加根号b=根号2009,且a大于b大于0,试求满足上式的整数对(a,b)的个数
2009 = 7*7*41
根号2009 = 7根号41
根号a + 根号b = 根号2009 = 7根号41
(1):根号a = 6根号41;根号b = 根号41
a = 1476;b = 41
(2):根号a = 5根号41;根号b = 2根号41
a = 1025;b = 164
(3):根号a = 4根号41;根号b = 3根号41
a = 656 ;b = 369
综上,有3种:
(1476,41)
(1025,164)
(656 ,369)
根号2009 = 7根号41
根号a + 根号b = 根号2009 = 7根号41
(1):根号a = 6根号41;根号b = 根号41
a = 1476;b = 41
(2):根号a = 5根号41;根号b = 2根号41
a = 1025;b = 164
(3):根号a = 4根号41;根号b = 3根号41
a = 656 ;b = 369
综上,有3种:
(1476,41)
(1025,164)
(656 ,369)
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