X平方+根号3Y=根号5,Y平方+根号3X=根号5,
X^2+√3Y=Y^2+√3X,
X^2-Y^2+√3(Y-X)=0,
(X+Y)(X-Y)+√3(Y-X)=0,
X+Y-√3=0,
Y=√3-X,
X^2+√3*(√3-X)=√5.
X^2-√3X+3-√5=0,X^2-√3X=√5-3.
X分之Y+Y分之X
=(X^2+Y^2)/XY
=[X^2+(√3-X)^2/[X*(√3-X)]
=[2(X^2-√3X)+3]/[-(X^2-√3X].
而,X^2-√3X=√5-3.
[2(X^2-√3X)+3]/[-(X^2-√3X].
=[2*(√5-3)+3]/[-(√5-3)]
=(2√5-3)/[-(√5-3)]
=(1+3√5)/4.
即,X分之Y+Y分之X的值=(1+3√5)/4.