美夢成真教甄討論區

請參考附件


第 17 題 條件不足，應送分

老師好 想請問17,32,33,35謝謝老師

第 32 題
3a^2 + 2a - 4 = 0
a = (-1 ± √13) / 3
a^2 = (14 ± 2√13) / 9

b^4 - b^2 - 3 = 0
b^2 = (1 + √13) / 2

(a^2b^4 + 4) / a^2 = b^4 + (4 / a^2) = b^2 + 3 + (4 / a^2) = 7 或 7 + √13


第 33 題
利用 x^4 + 4y^4
= (x^2 - 2xy + 2y^2)(x^2 + 2xy + 2y^2)
= [(x - y)^2 + y^2][(x + y)^2 + y^]
改寫分子和分母那八項，約分後剩 (49^2 + 3^2) / (1^2 + 3^2) = 241


第 35 題
ab + 5 = c
bc + 1 = a
ca + 1 = b

a - bc = b - ca
a - bc - b + ca = 0
(a - b)(c + 1) = 0

(1) a = b
c = a^2 + 5
a(a^2 + 5) + 1 = a
a^3 + 4a + 1 = 0，無整數解，不合

(2) c = -1
ab = -6
a + b = 1
(a，b) = (3，-2) 或 (-2，3)