1/x+1/y=5, (x+y)/xy=5, x+y=5xy, 5xy-x=y, x(5y-1)=y, x=y/(5y-1), x^2=y^2/(25y^2-10y+1).
1/x^2+1/y^2=13, (x^2+y^2)/x^2y^2=13, x^2+y^2=13x^2y^2.
y^2/(25y^2-10y+1)+y^2=13y^4/(25y^2-10y+1), y^2*(25y^2-10y+1)+y^2=13y^4, 25y^4-10y^3+y^2+y^2=13y^4, 12y^4-10y^3+2y^2=0, 6y^2-5y+1=0, D=25-24=1, y1=(5-1)/12=1/3, y2=(5+1)/12=1/2.
x1=(1/3)/(5/3-1)=(1/3)/(2/3)=1/2, x2=(1/2)/(5/2-1)=(1/2)/(3/2)=1/3.
1/x+1/y=5, (x+y)/xy=5, x+y=5xy, 5xy-x=y, x(5y-1)=y, x=y/(5y-1), x^2=y^2/(25y^2-10y+1).
1/x^2+1/y^2=13, (x^2+y^2)/x^2y^2=13, x^2+y^2=13x^2y^2.
y^2/(25y^2-10y+1)+y^2=13y^4/(25y^2-10y+1), y^2*(25y^2-10y+1)+y^2=13y^4, 25y^4-10y^3+y^2+y^2=13y^4, 12y^4-10y^3+2y^2=0, 6y^2-5y+1=0, D=25-24=1, y1=(5-1)/12=1/3, y2=(5+1)/12=1/2.
x1=(1/3)/(5/3-1)=(1/3)/(2/3)=1/2, x2=(1/2)/(5/2-1)=(1/2)/(3/2)=1/3.