已知实数a,b满足a^2-7a+2=0,b^2-7b+2=0,则b/a+a/b=?

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已知实数a,b满足a^2-7a+2=0,b^2-7b+2=0,则b/a+a/b=?
已知实数a,b满足a^2-7a+2=0,b^2-7b+2=0,则b/a+a/b=?

已知实数a,b满足a^2-7a+2=0,b^2-7b+2=0,则b/a+a/b=?
a^2-7a+2=0
b^2-7b+2=0
两式相减
a^2-7a+2=0
b^2-7b+2=0
两式相减
a^2-b^2=7(a-b)
a+b=7
两式相加
a^2+b^2-7(a+b)+4=0
（a+b)^2-2ab-7(a+b)+4=0
7^2-2ab-7x7+4=0
ab=2
a^2+b^2=(a+b)^2-2ab=7^2-2x2=45
则b/a+a/b
=b^2+a^2/ab
=45/2
请仔细看,思路没问题,

由题可知,a,b为方程x^2-7x+2=0的解
则a+b=7,ab=2
则b/a+a/b=(a^2+b^2)/ab=[(a+b)^2-2ab]/ab=45/2

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