Question

【关于韦达定理 x1,x2为方程2x^2-6x+3=0两根,求x1^3-x2^3

Answer 1

x1,x2是方程 2x^2-6x+3=0 两根,则 x1+x2=3,x1x2=3/2,

x1-x2= ±√[(x1+x2)^2-4x1x2]=±√(9-6)=±√3

x1^3-x2^3 = (x1-x2)(x1^2+x1x2+x2^2) =±√3[(x1+x2)^2-x1x2]

= ±√3(9-3/2) = ±(15/2)√3