請問這題數學怎麼解?

[匿名]

2011-08-06 8:07 am

數學強的同學幫幫忙吧!我家老大發問,剛好數學我最爛..... .[(2^4+1/4) (4^4+1/4) (6^4+1/4) (8^4+1/4) (10^4+1/4)]÷[ (1^4+1/4) (3^4+1/4) (5^4+1/4) (7^4+1/4) (9^4+1/4)]這題怎麼解?謝謝了!!

回答 (1)

用戶2053

2011-08-06 8:40 am

✔ 最佳答案

x⁴ + 1/4
= x⁴ + 2(1/2)x² + 1/4 - x²
= (x² + 1/2)² - x²
= (x² - x + 1/2) (x² + x + 1/2)
= [(x - 1/2)² + 1/4] [(x + 1/2)² + 1/4]

所以[(2⁴+ 1/4) (4⁴+ 1/4) (6⁴+ 1/4) (8⁴+ 1/4) (10⁴+ 1/4)]
÷
[(1⁴+ 1/4) (3⁴+ 1/4) (5⁴+1/4) (7⁴+1/4) (9⁴+1/4)]= (1.5² + 1/4)(2.5² + 1/4) (3.5² + 1/4)(4.5² + 1/4) (5.5² + 1/4)(6.5² + 1/4)
(7.5² + 1/4)(8.5² + 1/4) (9.5² + 1/4)(10.5² + 1/4)
÷
(0.5² + 1/4)(1.5² + 1/4) (2.5² + 1/4)(3.5² + 1/4) (4.5² + 1/4)(5.5² + 1/4)
(6.5² + 1/4)(7.5² + 1/4) (8.5² + 1/4)(9.5² + 1/4)=(10.5² + 1/4) / (0.5² + 1/4)= 110.5 / 0.5= 221

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