设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3

设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3
设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3

设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3
x1 x2是方程2x^2-6x+3=0的两个根,
∴x1+x2=-6÷(-2)=3
x1x2=3/2
x1^3+x2^3
=(x1+x2)(x1²-x1x2+x2²)
=(x1+x2)[(x1²+2x1x2+x2²)-3x1x2]
=(x1+x2)[(x1+x2)²-3x1x2]
=3×(3²-3×3/2)
=27/2