x^2-ax+4=0(a错了,题目是求√(x1\x2)+√(x2\x1)

问题描述:

x^2-ax+4=0(a
错了,题目是求√(x1\x2)+√(x2\x1)

x^2-ax+4=0(ax1x2=4,x1+x2=a
a题目错

由根与系数的关系,得:
x₁+x₂=a
x₁*x₂=4
则有:
[√(x₁/x₂)+√(x₂/x₁)]&sup2
=(x₁/x₂)+(x₂/x₁)+2
=(x₁&sup2+x₂&sup2)/(x₁*x₂)+2
=(x₁&sup2+x₂&sup2+2x₁*x₂-2x₁*x₂)/4+2
=[(x₁+x₂)&sup2-2x₁*x₂]/4+2
=[a&sup2-8]/4+2
=a&sup2/4
由于a