Question

已知a=根号5-2,b=根号5-2,求a分之b+b分之a+2的值

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Answer 1

a分之b+b分之a+2
=b/a+a/b+2
=(b²+a²+2ab)/ab
=(a+b)²/ab
a=根号5+2，b=根号5-2
a+b=2√5
ab=(根号5+2)(根号5-2)=5-4=1代入得
(a+b)²/ab
=(2√5)²/1
=20
希望能解决您的问题。

Answer 2

a+b=根号5-2+根号5+2=2根号5 a、b中把一个改成+2
ab=(根号5-2)(根号5+2)=1

原式=(b²/ab+a²/ab+2ab/ab
=(a²+2ab+b²)/ab
=(a+b)²/ab
=(2根号5)²/1
=20

Answer 3

a=√5+2,b=√5-2
b/a+a/b+2
=(a²+b²)/(ab)+2
=(a+b)²/(ab)-2+2
=(2√5)²/[(√5+2)(√5-2)]
=20