Question

若正数x,y满足x平方-y平方=2xy,求x-y除以x+y的值

Answer 1

因为正数x,y满足x平方-y平方=2xy,

所以

(x^2-y^2)=2xy

即

1-(y/x)^2=2(y/x)

(y/x)^2+2(y/x)-1=0

y/x=[-2+√(4+4)]/2=-1+√2 (因为x,y为正数,所以取y/x>0的根)

(x-y)/(x+y)=(1-y/x)/(1+y/x)

=(1+1-√2)/(√2)

=(2-√2)/√2

=√2-1.