已知实数a,b满足a^2-3a+1=0,b^2-3b+1=0,求a/b+b/a的值

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已知实数a,b满足a^2-3a+1=0,b^2-3b+1=0,求a/b+b/a的值已知实数a,b满足a^2-3a+1=0,b^2-3b+1=0,求a/b+b/a的值已知实数a,b满足a^2-3a+1=

已知实数a,b满足a^2-3a+1=0,b^2-3b+1=0,求a/b+b/a的值
已知实数a,b满足a^2-3a+1=0,b^2-3b+1=0,求a/b+b/a的值

已知实数a,b满足a^2-3a+1=0,b^2-3b+1=0,求a/b+b/a的值
设a、b是方程:x²-3x+1=0的两个根.
则有:a²-3a+1=0
b²-3b+1=0
a+b=3
ab=1
∴ a/b+b/a=﹙a²+b²﹚/ab
=a²+b²
=﹙a+b﹚²-2ab
=3²-2
=7.