※ 引述《deryann (星辰)》之銘言：
: 1/x + 1/2y = (x^2+3y^2)(3x^2+y^2)
: 1/x - 1/2y = 2(y^4 - x^4)
: 如何解 x, y
: 先謝過各位高手了!!
1/x + 1/2y = 3x^4+10x^2y^2+3y^4
1/x - 1/2y =-2x^4 +2y^4
相加得2/x = x^4 + 10x^2y^2 + 5y^4 => 2 = x^5 +10x^3y^2 + 5xy^4 ... (1)
相減得1/y =5x^4 + 10x^2y^2 + y^4 => 1 =5x^4y+10x^2y^3 + y^5 ... (2)
(1)+(2)得 3= (x+y)^5 => x+y = 3^(1/5)
(1)-(2)得 1= (x-y)^5 => x-y = 1
故x=(1/2)(3^(1/5)+1), y=(1/2)(3^(1/5)-1)
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