Question

1、正数X,Y,满足x平方+y平方=2xy,求(x-y)/(x+y)

Answer 1

x^2-y^2=2xy

x^2-2xy-y^2=0

x=(1±√2)y

(x-y)/(x+y)

=((1±√2)y-y)/((1±√2)y+y)

=±√2/(2±√2)

=±1/(√2±1)

=√2-1 or -√2+1

令3t^2+4t-1=0

t=(-2±√7)/3

故3x^2+4xy-y^2

=(x-t1y)(x-t2y)

=[x+(2-√7)/3*y][x+(2+√7)/3*y]