解方程5x²-5x+1=0,得两根x1=(5-√5)/10,x2=(5+√5)/10,故5x²-5x+1=5(x-x1)(x-x2).故5x²-5xy+y²=y²(5(x/y)²-5(x/y)+1)
=5y²(x/y-x1)(x/y-x2)
=5(x-x1y)(x-x2y)
=5(x-[(5-√5)/10]y)(x-[(5+√5)/10]y)