數學問題集(54)---數學雜題(一)

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圖片參考：http://img529.imageshack.us/img529/7914/88465774.png


2010-10-06 20:47:33 補充：
http://img529.imageshack.us/img529/7914/88465774.png

(x + y)^2 = 1^2
x^2 + 2xy + y^2 = 1
xy = -1/2

(x + y)(x^2 + y^2) = 1*2
x^3 + y^3 + xy(x + y) = 2
x^3 + y^3 = 5/2

(x^2 + y^2)^2 = 2^2
x^4 + 2(xy)^2 + y^4 = 4
x^4 + y^4 = 7/2

(x^3 + y^3)(x^4 + y^4) = (5/2)(7/2)
x^7 + y^7 + (xy)^3(x + y) = 35/4
x^7 + y^7 = 71/8

1) 2(a^2 + ab + b^2)^2

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3)

5/9 ~ 56 %