Re: [中學] 高中數學

看板Math作者a016258 (憨)時間8年前 (2015/11/02 18:56)推噓0(0推 0噓 7→)

留言7則, 2人參與討論串66/91 (看更多)

※ 引述《semmy214 (陳山河)》之銘言： : http://imgur.com/YAUm71e

: 第1題不用回答 : 2、3、4煩請版上高手解答 2. θ 省略... sin^m = ( sin θ)^m x^2 + y^2 = cos^6 + (sin^6 + 2sin^4 + sin^2) (三次方和拆前兩項) = (cos^4 - cos^2 sin^2 + sin^4) + 2sin^4 + sin^2 (合併二、五項) = cos^4 + 4 sin^4 = (cos^2 + 2sin^2 )^2 - 4sin^2 cos^2 = sin^4 + 2sin^2 + 1 - 4sin^2 cos^2 = sin^4 + 2sin^2 + 1 - 4sin^2 (1 - sin^2 ) = 5sin^4 - 2sin^2 + 1 = 5( sin^2 - (1/5) )^2 + 4/5 when sin^2 = 1/5 , min = 2/√5 when sin^2 = 1 , max = 2 4. f(x) = sinx cosx + a(sinx + cosx) + a^2 ( t = sinx + cosx ≦ √2 ) = (t^2 - 1)/2 + at + a^2 = (1/2) (t^2 + 2at + 2a^2 - 1) ( ∵ a ≧ 0 ) ≦(1/2) ( 2 + 2√2 a + 2a^2 - 1) = (1/2) (2a^2 + 2√2 a + 1) = 25/2 => a^2 + √2 a - 12 = 0 -√2 + √50 a = --------------- = 2√2 2 有錯還請不吝指正。 -- If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. － John von Neumann -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 140.114.137.240 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1446461803.A.3FC.html ※ 編輯: a016258 (140.114.137.240), 11/02/2015 19:03:32

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semmy214

11/02 19:04, , 1^F

11/02 19:04, 1^F

cos^6 + sin^6 = (cos^2 )^3 + (sin^2 )^3 三次方和化成兩項相乘 ※ 編輯: a016258 (140.114.137.240), 11/02/2015 19:06:27

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semmy214

11/02 19:10, , 2^F

11/02 19:10, 2^F

(a+b) = ?

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Eliphalet