已知方程2x²-3x-1=0的两根为x₁,x₂则x₁-x₂=

已知方程2x²-3x-1=0的两根为x₁,x₂则x₁-x₂=
已知方程2x²-3x-1=0的两根为x₁,x₂则x₁-x₂=

已知方程2x²-3x-1=0的两根为x₁,x₂则x₁-x₂=
x1+x2=3/2;
x1x2=-1/2;
x1-x2=±√(x1+x2)²-4x1x2=±√(9/4+2)=±√17/2;

x₁+x₂=3/2,x₁x₂=-1/2
|x₁-x₂|²=x₁²-2x₁x₂+x₂²
=x₁²+2x₁x₂+x₂²-4x₁x₂
=(x₁+x₂)²-4x₁x₂
=9/4+2
=17/4
x₁-x₂=(±√17)/2

2x²-3x-1=0的两根为x₁,x₂
∴x1+x2=3/2
x1x2=-1/2
(x1-x2)²
=x1²-2x1x2+x2²
=x1²+2x1x2+x2²-4x1x2
=(x1+x2)²-4x1x2
=9/4+2
=17/4
∴x1-x2=±√17/2