a + b + c = 2 và a^2 + b^2 + c^2 = 2. Tính a^4 + b^4 + c^4
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53 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