若实数a,b满足1/a-1/b=1/(a+b)则b/a+a/b等于

Question

若实数a,b满足1/a-1/b=1/(a+b)则b/a+a/b等于

Answer 1

由1/a-1/b=1/(a+b)两边乘以（a+b）得：
178（a+b）/a-（a+b）/b=1,即;b/a-a/b=1
b/a-a/b=1两边平方得：b²/a²-2*（b/a）*（a/b）+a²/b²=1
得：b²/a²+a²/b²=3
所以b/a+a/b=√(b/a+a/b)²
=√[b²/a²+2*(b/a)*(a/b)+a²/b²]²
=√(3+2)
=√5