美夢成真教甄討論區

請參考附件

計算第 3 題 (2)
x^2 - y - 6 = 0
x + 2(y - 30)^2 - 6 = 0
2(x^2 - y - 6) + x + 2(y - 30)^2 - 6 = 0
(x + 1/4)^2 + (y - 61/2)^2 = 629/16
r 的最小值為 √629 / 4

計算第 2 題 (2)
x^2/(y + z) + y^2/(z + x) + z^2/(x + y) = 0

同乘以 (x + y)(y + z)(z + x)
x^2(x + y)(z + x) + y^2(x + y)(y + z) + z^2(y + z)(z + x) = 0

乘開後可分解成
(x + y + z)(x^3 + y^3 + z^3 + xyz) = 0
x + y + z ≠ 0
x^3 + y^3 + z^3 = -xyz
x^2/(yz) + y^2/(zx) + z^2/(xy) = -1