已知xy不等於0,x²+y²=1,試找出(x^4+y^4)/(x^5+y^5),(x^4+y^4)/√(x^6+y^6) 與√(x^4+y^4)/(x^6+y^6)三者之大小關係?

代入x = 0.6, y = +/-0.8 ,x²+y² =0.36+0.64=1
(x^4+y^4)/√(x^6+y^6) = 0.5392/√0.3088 = 0.9703
(x^4+y^4)/(x^5+y^5) = 0.5392/0.40544 = 1.3299 或 0.5392/-0.24992 = -2.1575
√(x^4+y^4)/(x^6+y^6) = √0.5392/0.3088 = 2.3779
x = 0.6, y = 0.8 則(x^4+y^4)/√(x^6+y^6) < (x^4+y^4)/(x^5+y^5) < √(x^4+y^4)/(x^6+y^6)
x = 0.6, y = -0.8 則(x^4+y^4)/(x^5+y^5) < (x^4+y^4)/√(x^6+y^6) < √(x^4+y^4)/(x^6+y^6)