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這種題目要試著把現有的條件“沾上邊”

知道a^2 + b^2 + c^2 = 9，那麼要如何從a - b + c當變出a^2 + b^2 + c^2 ?

既然是變出平方，就試著把a - b + c = 1兩邊同時平方
(a - b + c)^2 = 1^2 = 1

左邊展開得到
a^2 + b^2 + c^2 -2ab + 2ac - 2bc
右邊還是1

整理
=>
(a^2 + b^2 + c^2) -2(ab - ac + bc) = 1

=>
9 -2(ab - ac + bc) = 1

=>
2(ab - ac + bc) = 8

=>
ab - ac + bc = 4

參考資料 自己

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