若实数a,b满足a²+ab-b²=0,则a/b=

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若实数a,b满足a²+ab-b²=0,则a/b=
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若实数a,b满足a&sup2;+ab-b&sup2;=0,则a/b=
若实数a,b满足a&sup2;+ab-b&sup2;=0,则a/b=

若实数a,b满足a&sup2;+ab-b&sup2;=0,则a/b=
a=b=0时,等式成立,a/b无意义.
a≠0且b≠0时,
a²+ab-b²=0
等式两边同除以b²
(a/b)²+(a/b) -1=0
(a/b)²+(a/b)=1
(a/b)²+(a/b)+1/4=5/4
(a/b +1/2)²=5/4
a/b=(√5-1)/2或a/b=-(√5+1)/2