Question

实数m取何值时,关于x的方程x^2-(m-2)x+(m+3)=0的两根平方和最小?并求出这个最小值．

Answer 1

设两根为x1,x2,

x1^2+x2^2

=(x1+x2)^2-2x1*x2

=(m-2)^2-2(m+3)

=m^2-10m-2

=(m-5)^2-27

当m=5时,最小值-27