推 knuk : 感謝 12/20 02:22
※ 引述《knuk (金鋒)》之銘言：
: a,b,c相異，滿足下式
: a^3+b^3+2(a^2+b^2)=b^3+c^3+2(b^2+c^2)=a^3+c^3+2(a^2+c^2)
: 求a+b+c
: 麻煩大家幫忙了，感謝
(a - c)(a^2 + ac + c^2) = 2(c + a)(c - a)
=> (a - c)[a^2 + ac + c^2 + 2a + 2c] = 0
=> (a + 1)^2 + (c + 1)^2 + ac = 2
同理(b + 1)^2 + (c + 1)^2 + bc = 2
=> (a + b + c + 2)(a - b) = 0
=> a + b + c = -2
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