close
標題:
IMO---1960(inequality)
發問:
Please refer to the following question: 圖片參考：http://hk.geocities.com/stevieg_1023/IMO1960.gif
最佳解答:
For the function to be well defined, we must have x>-1/2 and x≠0. Suppose x satisfies these conditions, then 4x^2 / (1-√(1+2x))^2 < 2x+9 ? 4x^2 < (2x+9)(1-√(1+2x))^2 = (2x+9)(1+(1+2x)-2√(1+2x)) ? 2x^2 < (2x+9)(1+x-√(1+2x)) = 2x^2 + 11x + 9 -(2x+9)√(1+2x) ? (2x+9)√(1+2x) < 11x+9 Since x>-1/2, 2x+9 > 0. and 11x+9 > 0, so the above inequality is equivalent to (2x+9)^2 (1+2x) < (11x+9)^2 (4x^2 + 36x + 81)(2x+1) < (121x^2 + 198x + 81) 8x^3 + 76x^2 + 198x + 81 < 121x^2 + 198x + 81 8x^3 - 45x^2 < 0 8x - 45 < 0 x < 45/8. Therefore the solution is -1/2 < x < 45/8 and x≠0, i.e., 0 < x < 45/8 or -1/2 < x < 0
![]()
其他解答:E2A5F59BAA12C031
IMO---1960(inequality)
發問:
Please refer to the following question: 圖片參考：http://hk.geocities.com/stevieg_1023/IMO1960.gif
最佳解答:
For the function to be well defined, we must have x>-1/2 and x≠0. Suppose x satisfies these conditions, then 4x^2 / (1-√(1+2x))^2 < 2x+9 ? 4x^2 < (2x+9)(1-√(1+2x))^2 = (2x+9)(1+(1+2x)-2√(1+2x)) ? 2x^2 < (2x+9)(1+x-√(1+2x)) = 2x^2 + 11x + 9 -(2x+9)√(1+2x) ? (2x+9)√(1+2x) < 11x+9 Since x>-1/2, 2x+9 > 0. and 11x+9 > 0, so the above inequality is equivalent to (2x+9)^2 (1+2x) < (11x+9)^2 (4x^2 + 36x + 81)(2x+1) < (121x^2 + 198x + 81) 8x^3 + 76x^2 + 198x + 81 < 121x^2 + 198x + 81 8x^3 - 45x^2 < 0 8x - 45 < 0 x < 45/8. Therefore the solution is -1/2 < x < 45/8 and x≠0, i.e., 0 < x < 45/8 or -1/2 < x < 0
- 我想要一個靚錢包-@1@
- 咩防曬最好呢-（１０分）
- 點計subnet mask@1@
- pokemon遺傳_5@1@
- 有２０點！！！！我想要長笛譜啊@1@
- 死神 bleach主題曲 -@1@
- 驅鬼方法(佛教的)@1@
- 忍豆風雲2ac 20分@1@
- Double integral@1@
- 有冇火車去英德from深圳,請顯示班次和時間@1@
此文章來自奇摩知識+如有不便請留言告知
文章標籤
全站熱搜
留言列表
