北京初中数学竞赛题解方程。直接去分母？学霸换元的解法很巧妙

[@年年鱼]

令y = 4x/(x+4) => xy = 4(x-y) ----① 代入原式得 x² + y² = 20 -----② ② - ① x 2 x² + y² - 2xy = 20 - 8(x-y) (x - y)² +8(x-y) - 20 = 0 (x - y + 10)(x - y - 2) = 0 ∴ x - y + 10 = 0 或 x - y - 2 = 0 联合①式 x - y + 10 = 0 y = 4x/(x+4) 无实根 x - y - 2 = 0 y = 4x/(x+4) 解得x = 4 或 x = -2