已知3x的平方-x-4=0不算方程.求：（1）x1+x2的平方（2)(x1-3)(x2-3)（3）（x1-x2）的平方（4）x1的平方分之1+x2的平方分之1

Question

Answer 1

3x的平方-x-4=0
根据根与系数的关系得
x1+x2=1/3
x1x2=-4/3
x1^2+x2^2
=(x1+x2)^2-2x1x2
=1/9+8/3
=25/9
(x1-3)(x2-3)
=x1x2-3(x1+x3)-9
=-4/3-1-9
=-11又1/3
(x1-x2)^2
=(x1+x2)^2-4x1x2
=1/9+16/3
=49/9
1/x1^2+1/x2^2
=(x1^2+x2^2)/(x1^2*x2^2)
=(25/9)/(16/9)
=25/16