標題:
中四數學題 二元二次方程
發問:
(A) 設X+1/X = A 以A表示X^2 + 1/X^2 (B) 解方程 6(X^2 + 1/X^2) - 5 (X + 1/X) - 38 = 0
最佳解答:
a. x + 1/x = A (x + 1/x)^2 = A^2 x^2 + 2 + 1/x^2 = A^2 x^2 + 1/x^2 = A^2 - 2 b. By a, 6(A^2 - 2) - 5A - 38 = 0 6A^2 - 5A - 50 = 0 A = 10/3 or -5/2 x + 1/x = 10/3 or x + 1/x = -5/2 3x^2 - 10x + 3 = 0 or 2x^2 + 5x + 2 = 0 x = 3,1/3 or -1/2,-2
中四數學題 二元二次方程
發問:
(A) 設X+1/X = A 以A表示X^2 + 1/X^2 (B) 解方程 6(X^2 + 1/X^2) - 5 (X + 1/X) - 38 = 0
最佳解答:
a. x + 1/x = A (x + 1/x)^2 = A^2 x^2 + 2 + 1/x^2 = A^2 x^2 + 1/x^2 = A^2 - 2 b. By a, 6(A^2 - 2) - 5A - 38 = 0 6A^2 - 5A - 50 = 0 A = 10/3 or -5/2 x + 1/x = 10/3 or x + 1/x = -5/2 3x^2 - 10x + 3 = 0 or 2x^2 + 5x + 2 = 0 x = 3,1/3 or -1/2,-2
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