Question

第一个,已知x1 x2是方程3x方-2x-7=0的两个根,不解方程,利用根与系数的关系,求(x1-x2)方

Answer 1

1）x1+x2=2/3 x1*x2=-7/3

(x1-x2)^2=x1^2-2x1x2+x2^2

=x1^2+2x1x2+x2^2-4x1x2

=(x1+x2)^2-4x1x2

=4/9-4*(-7/3)

=88/9

2)

x1+x2=2/3 x1*x2=-7/3

(x1-1/x2)(x2+1/x1)

=x1x2+1-1-1/(x1x2)

=x1x2-1/(x1x2)

=-7/3+3/7

=-40/21

3)

x1+x2=2/3 x1*x2=-7/3

x2/x1+x1/x2

=(x2^2+x1^2)/(x1x2)

=[(x1+x2)^2-2x1x2]/(x1x2)

=[4/9-2*(-7/3)]/(-7/3)

=(46/9)/(-7/3)

=-46/21