Question

tìm a,b thuộc Z biết : ab+1=2a+3b

 

Answer 1

 

Đáp án:

 (b,a)∈{(3,8),(7,4),(1,−2),(−3,2)}(b,a)∈{(3,8),(7,4),(1,−2),(−3,2)} 

Các bước giải:

ab+1=2a+3bab+1=2a+3b

→(ab−3b)+1=(2a−6)+6→(ab−3b)+1=(2a−6)+6 

→b(a−3)=2(a−3)+5→b(a−3)=2(a−3)+5 

→b(a−3)−2(a−3)=5→b(a−3)−2(a−3)=5 

→(b−2)(a−3)=5→(b−2)(a−3)=5 

→(b−2,a−3)∈U(5)={(1,5),(5,1),(−1,−5),(−5,−1)}→(b−2,a−3)∈U(5)={(1,5),(5,1),(−1,−5),(−5,−1)} 

→(b,a)∈{(3,8),(7,4),(1,−2),(−3,2)}→(b,a)∈{(3,8),(7,4),(1,−2),(−3,2)} 

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