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幫幫手﹏plz!!
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解以下方程。如有須要,答案準確至3位有效數字。(a) x^4 - 3x^2 - 4 =0(b) x-4/x=2(c) 開方x-1 =x-3(d) (x+1)^2 - 4(x+1) - 5=0(e) { y=x^2-2x-3 x+y-3=0(f) { 3x^2+2y+1=0 3y-4x=41(g) 3/x-1 + x+1/x+3 = 8/x^2+2x-3(h) x+2x/x-3 = 6/x-3(2) 瑪莉有＄９６，可以買ｋ個橙。若侮個橙的售價調低＄２，她便可多買４個橙。求ｋ的值。幫下忙唔該哂﹏/\\/\\" 顯示更多 解以下方程。如有須要,答案準確至3位有效數字。 (a) x^4 - 3x^2 - 4 =0 (b) x-4/x=2 (c) 開方x-1 =x-3 (d) (x+1)^2 - 4(x+1) - 5=0 (e) { y=x^2-2x-3 x+y-3=0 (f) { 3x^2+2y+1=0 3y-4x=41 (g) 3/x-1 + x+1/x+3 = 8/x^2+2x-3 (h) x+2x/x-3 = 6/x-3 (2) 瑪莉有＄９６，可以買ｋ個橙。若侮個橙的售價調低＄２，她便可多買４個橙。求ｋ的值。 幫下忙唔該哂﹏/\\/\\"
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最佳解答:
(a) x^4 - 3x^2 - 4 =0 (x^2 - 4)(x^2 + 1) = 0 x^2 = 4 or x^2 = -1 (rejected) x = 2 or x = -2 (b) x-4/x=2 x-4 = 2x x = -4 (c) sqrt(x-1) =x-3 x-1 = (x-3)^2 x-1 = x^2 - 6x + 9 x^2 - 7x + 10 = 0 (x - 2)(x - 5) = 0 x = 2 or x = 5 當 x = 2, L.H.S = sqrt(1) = 1 R.H.S. = 2-3 = -1 rejected 當 x = 5, L.H.S = sqrt(4) = 2 R.H.S. = 5-3 = 2 所以 x = 5 (d) (x+1)^2 - 4(x+1) - 5=0 [ (x+1) - 5 ] [ (x+1) + 1 ] = 0 (x - 4)(x + 2) = 0 x = 4 or x = -2 (e) y=x^2-2x-3 x+y-3=0 y = -x + 3 -x + 3 = x^2-2x-3 x^2-x-6 = 0 (x - 3)(x + 2) = 0 x = 3 or x = -2 x = 3 , y = 0 x = -2, y = 5 (3, 0), (-2, 5) (f) 3x^2+2y+1=0 3y-4x=41 y = (4x + 41) / 3 3x^2+2(4x + 41) / 3+1=0 9x^2 + 2(4x + 41) +3=0 9x^2 + 8x + 85=0 無根, 係咪打錯野,計唔到 (g) 3/(x-1) + (x+1)/(x+3) = 8/(x^2+2x-3) 3/(x-1) + (x+1)/(x+3) = 8/[ (x-1) (x+3) ] [ 3(x+3) + (x+1)(x-1) ] / [ (x-1) (x+3) ] = 8/[ (x-1) (x+3) ] 3(x+3) + (x+1)(x-1) = 8 x^2 + 3x + 8 = 8 x^2 + 3x = 0 x(x + 3) = 0 x = 0 or x = -3 (rejected, 因為令分母變零) (h) x+2x/(x-3) = 6/(x-3) x(x-3) + 2x = 6 x^2 -x - 6 = 0 (x - 3)(x + 2) = 0 x = 3 (rejected, 令分母變零) or x = -2 2) 每個橙原本的售價 = 96/k 調低＄２,即新價 (96/k - 2), 可買 (k+4) 個橙,所以 (96/k - 2)(k+4) = 96 (96 - 2k)(k+4) = 96k (全式乘 k) -2k^2 + 88k + 384 = 96k 2k^2 - 8k - 384 = 0 k^2 - 4k - 192 = 0 (k - 16)(k + 12) = 0 k = 16 or k = -12 (rejected) 好多, 做死人
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