设方程3x^2-9x-1=0的两个根x1和x2,求x1x2^2+X1^2X2的值 和 绝对值x1-x2的值

Question

设方程3x^2-9x-1=0的两个根x1和x2,求x1x2^2+X1^2X2的值 和 绝对值x1-x2的值

Answer 1

∵3x^2-9x-1=0的两个根是 x1和x2,
∴x1+x2=3,
x1x2=-1/3
x1x2²+x1²x2
=x1x2(x2+x1)
=(-1/3)×3
=-1
|x1-x2|
=√(x1-x2)²
=√[(x1+x2)²-4x1x2]
=√[3²-4×(-1/3)]
=√[9+(4/3)]
=√(39/4)
=½√39