作业帮若x^y-2xy+y+x^2-2x=1983,求满足条件的整数对(x,y)....
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若x^y-2xy+y+x^2-2x=1983,求满足条件的整数对(x,y)....
若x^y-2xy+y+x^2-2x=1983,求满足条件的整数对(x,y)
....
若x^y-2xy+y+x^2-2x=1983,求满足条件的整数对(x,y)....
x^y-2xy+y+x^2-2x=1983
x^2(y+1)-2x(y+1)+(y+1)=1984
(x-1)^2(y+1)=1984
1984=4*496=16*124=64*31
所以,
y+1=496,y=495时,
(x-1)^2=4,x-1=±2,x=3,或,x=-1
y+1=124,y=123时,
(x-1)^2=16,x-1=±4,x=5,或,x=-3
y+1=31,y=30时,
(x-1)^2=64,x-1=±8,x=9,或,x=-7
满足条件的整数对:
-1,495）,（3,495）,（-3,123）,（5,123）,（-7,30）,（9,30）
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