设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3
问题描述:
设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3
答
x1 x2是方程2x^2-6x+3=0的两个根,∴x1+x2=-6÷(-2)=3x1x2=3/2x1^3+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...