Toán Lớp 8: Tìm x
(x + 3)^4 + (x + 5)^4 = 16
(x + 3)^4 + (x − 1)^4 = 626
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Toán Lớp 8: Tìm x
(x + 3)^4 + (x + 5)^4 = 16
(x + 3)^4 + (x − 1)^4 = 626
Comments ( 1 )
⇔ (t^4 − 4t^3 + 6t^2 − 4t + 1) + (t^4 + 4t^3 + 6t^2 + 4t + 1) = 16
⇔ 2t^4 +12t^2 −14 = 0
⇔ t^2.(t^2 − 1) + 7.(t^2 − 1) = 0
⇔ (t − 1).(t + 1).(t^2 + 7) = 0 (t^2 + 7 > 0 ∀ t)
⇔ t = 1,t = −1
Vậy phương trình có nghiệm S = {-3; -5}
⇔ t^2.(t^2 − 9) + 33.(t^2 − 9) = 0
⇔ (t − 3).(t + 3).(t^2 + 33) = 0
Vậy phương trình có nghiệm S = {2, -4}
(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
(a − b)^4 = a^4 − 4a^3b + 6a^2b^2 − 4ab^3 + b^4