已知实数a.b满足a*a-3a=1,b*b-3b=1,求2b/a+2a/b的值
问题描述：
已知实数a.b满足a*a-3a=1,b*b-3b=1,求2b/a+2a/b的值
答
a,b是方程x^2-3x-1=0的两个根
所以ab=-1
a+b=3
a*a-3a=1
a^2=1+3a
b*b-3b=1
b^2=1+3b
2b/a+2a/b
=(2a^2+2b^2)/ab
=2(a^2+b^2)/ab
=2(1+3a+1+3b)/ab
=2[2+3(a+b)]/ab
=2*[2+3*3]/(-1)
=-22