Question

已知方程x^2-x-1=0的两个根是x1,x2,求下列各式的值 ①x1乘x2^2+x1^2乘x2②（x1-x2)^2③x1^2+x2^2

Answer 1

已知方程x^2-x-1=0的两个根是x1,x2,
∴x1+x2=1
x1x2=-1
∴①x1乘x2^2+x1^2乘x2
=x1x2(x1+x2)
=-1

②（x1-x2)^2
=(x1+x2) ²-4x1x2
=1+4
=5
③x1^2+x2^2
=(x1+x2)²-2x1x2
=1+2
=3