Question

这三道解方程用什么方法解最简便?①x^2-3x -1=0②（3x -2）^2=(x +4)^2③（x -3）^2=2x

Answer 1

①x^2-3x -1=0

(x-3/2)^2-9/4-1=0

(x-3/2)^2=13/4

x-3/2=±√13/2

x=(3±√13)/2

②（3x -2）^2=(x +4)^2

3x-2=x+4或3x-2=-x-4

解得x=3或x=-0.5

③（x -3）^2=2x (3-x )

(x-3)^2=-2x(x-3)

(x-3)^2+2x(x-3)=0

(x-3)(x-3+2x)=0

(x-3)(3x-3)=0

解得x=3或x=1