MQ4 --- Factorization

👨🏻‍🏫 學術台數學

用戶27207

2012-05-01 4:17 am

Difficulty: 40%Factorize (x⁴ + 1/x⁴)/4 + 4x⁴/(x⁸ + 2x⁴ + 1) - 3/2

回答 (1)

[匿名]

2012-05-01 5:27 am

✔ 最佳答案

我想問係唔係咁???
我唔識做落去啦- -

圖片參考：http://latex.codecogs.com/gif.latex?\begin{align*}%20&%20\frac{(x^4+\frac{1}{x^4})}{4}+\frac{4x^4}{x^8+2x^4+1}-\frac{3}{2}\\%20&=\frac{y+\frac{1}{y}}{4}+\frac{4y}{(y+1)^2}-\frac{3}{2}%20\\%20&=%20\frac{y^2+1}{4y}+\frac{4y}{(y+1)^2}-\frac{3}{2}\\%20&=%20\frac{(y^2+1)(y+1)^2+16y^2-6y(y+1)^2}{4y(y+1)^2}\\%20&=%20\frac{(y^2+1)(y^2+2y+1)+16y^2-6y^3-12y^2-6y}{4y(y+1)^2}\\%20&=%20\frac{y^4-4y^3+6y^2-4y+1}{4y(y+1)^2}\\%20&=%20\frac{(y-1)^4}{4y(y+1)^2}\\%20&=%20\frac{(x^4-1)^4}{4x^4(x^4+1)^2}\\%20&=%20\frac{(x^2+1)^4(x+1)^4(x-1)^4}{4x^4(x^4+1)^2}\\%20\end{align*}

參考: 神風亨

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