Question

已知x1 x2是方程x²+3x+1=0的两根,则(x1)²-3(x2)²+20=_____

Answer 1

已知x1 x2是方程x²+3x+1=0的两根：

X1=(√5 - 3)/2,

X2=(-√5-3)/2

则：(X1)^2=(7-3√5)/2

(X2)^2=(7+3√5)/2

(X1)²-3(X2)²+20

=3.5-1.5√5-3(3.5+1.5√5)+20

=13-6√5