F.2 化簡分式 (15x2=30點)

考慮 : x^4 + 324= x^4 + 18^2= x^4 + 2(x^2)(18) + 18^2 - 2(x^2)(18)= (x^2 + 18)^2 - (6x)^2= (x^2 - 6x + 18)(x^2 + 6x + 18)= (x^2 - 6x + 9 + 9)(x^2 + 6x + 9 + 9)= [(x - 3)^2 + 9] [(x + 3)^2 + 9]
故(10^4+324) (22^4+324) / [(16^4+324) (28^4+324)]= [(10 - 3)^2 + 9] [(10 + 3)^2 + 9] [(22 - 3)^2 + 9] [(22 + 3)^2 + 9]
__________________________________________[(16 - 3)^2 + 9] [(16 + 3)^2 + 9] [(28 - 3)^2 + 9] [(28 + 3)^2 + 9]
= (7^2 + 9) (13^2 + 9) (19^2 + 9) (25^2 + 9)
_____________________________________(13^2 + 9) (19^2 + 9) (25^2 + 9) (31^2 + 9)
= (7^2 + 9) / (31^2 + 9)
= 58 / 970


2010-09-10 23:57:13 補充：
= 29 / 485

忘了約分。