已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=

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已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=已知实数a,b满足(a+b)^2=2b^

已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=
已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=

已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=
(a+b)^2=2b^2+ab
所以a^2+2ab+b^2=2b^2+ab
a^2-ab=b^2
a(a-b)=b^2
b/(a-b)=a/b
又a^2-ab=b^2
所以a^2-ab-b^2=0
把a看作未知数
a=(b±√5b^2)/2=b(1±√5)/2
a/b=(1±√5)/2
ab同号,所以a/b>0
a/b=(1+√5)/2
(a+b)/(a-b)=(a-b+2b)/(a-b)
=(a-b)/(a-b)+2b/(a-b)
=1+2b/(a-b)
=1+2a/b
=1+1+√5
=2+√5

(a+b)^2=2b^2+ab
所以a^2+2ab+b^2=2b^2+ab
a^2-ab=b^2
所以a(a-b)=b^2
a^2=b(a+b)
a+b/a-b=a^3/b^3

(a+b)/(a-b)=(a-b+2b)/(a-b)
=(a-b)/(a-b)+2b/(a-b)
=1+2b/(a-b)
=1+2a/b
=1+1+√5
=2+√5

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