x=3-√5,则代数式x²-6x+8的值是A.4 B.5 C.-4 D.-5

x=3-√5,则代数式x²-6x+8的值是A.4 B.5 C.-4 D.-5
x=3-√5,则代数式x²-6x+8的值是
A.4 B.5 C.-4 D.-5

x=3-√5,则代数式x²-6x+8的值是A.4 B.5 C.-4 D.-5
x-3=-√5
两边平方
x²-6x+9=5
两边减去1
x²-6x+8=4
选A

x^2-6x+8
=(x-3)^2-1
=(x-4)(x-2)
=(3-根号5-4)(3-根号5-2)
=-(1+根号5)(1-根号5)
=4