Question

已知函数f(x)= ln(x)/x的图像为曲线C,函数g(x)=1/2ax+b的图像为直线l,设直线l与曲线C的交点横坐

Answer 1

L与C交点横坐标满足lnx/x=(1/2)ax+b,

即(1/2)ax^2+bx=lnx(x>0),

∴（1/2）ax1^2+bx1=lnx1,

(1/2)ax2^2+bx2=lnx2,

相加得(1/2)a(x1^2+x2^2)+b(x1+x2)=ln(x1x2),

(x1+x2)g(x1+x2)-2

=(x1+x2)[(1/2)a(x1+x2)+b]-2

=(1/2)a(x1+x2)^2+b(x1+x2)-2

=ax1x2+ln(x1x2)-2>0