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Tính a^4 + b^4 + c^4


a + b + c = 2 và a^2 + b^2 + c^2 = 2. Tính a^4 + b^4 + c^4
 
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Tham khảo câu trả lời từ Trợ lý ảo Lazi
Ta có:
(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + ac + bc) = 2 + 2(ab + ac + bc)
Vì a + b + c = 2, nên ta có:
(ab + ac + bc) = (a + b + c)^2 - (a^2 + b^2 + c^2) = 2^2 - 2 = 2
Từ đó, ta có:
(a + b + c)^2 - 2(ab + ac + bc) = 2 - 2(2) = -2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b^2 + c^2
(a + b + c)^2 - 2(ab + ac + bc) = a^2 + b

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