Question

已知X=根号7+根号5分之1,Y=根号7-根号5分之一,求x/y+y/x

Answer 1

x=1/(√7+√5)=(√7-√5)/2

y=1/(√7-√5)=(√7+√5)/2

所以

x+y=(√7-√5)/2 + (√7+√5)/2=√7

xy=(√7-√5)/2 X (√7+√5)/2=1/2

x/y +y/x

=(x²+y²)/xy

=[(x+y)²-2xy]/xy

=(7-1)/(1/2)

=12