標題:
MATHS(解方程)
發問:
1. 解以下方程。 如有需要 , 答案準至3位有效數字(a) x^4 - 3x^2 - 4 = 0(b) x - 4/x = 2(c) √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) 顯示更多 1. 解以下方程。 如有需要 , 答案準至3位有效數字 (a) x^4 - 3x^2 - 4 = 0 (b) x - 4/x = 2 (c) √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)
(a) x4 - 3x2 - 4 = 0 (x2 – 4)(x2 + 1) = 0 (x – 2)(x + 2)(x2 + 1) = 0 x = 2 or x = -2 (b) x - 4/x = 2; x<>0 x2 – 4 = 2x x2 – 2x – 4 = 0 x = {2 +/-√ [22 + 4(1)(4)]}/2 x = 1 +/-√ 5 x = 3.24 or x = -1.24 (c) √(x - 1) = x - 3 x – 1 = (x – 3)2 x – 1 = x2 – 6x + 9 x2 – 7x + 10 = 0 (x – 2)(x – 5) = 0 x = 5 or x = 2 (rejected) since √1 <> -1 (d) (x + 1)2 - 4(x + 1) - 5 = 0 Let u = x + 1 u2 – 4 u – 5 = 0 (u – 5)(u + 1) = 0 u = 5 => x = 4 or u = -1 => x = -2 (e) { y = x2 - 2x – 3 … (1) { x + y - 3 = 0 … (2) Sub (1) into (2) x + x2 - 2x – 3 – 3 = 0 x2 – x – 6 = 0 (x – 3)(x + 2) = 0 x = 3 => y = 0 or x = -2 => y = 5 (f) {3x2+ 2y + 1 = 0 … (1) {3y - 4x = 41 y = (41 + 4x)/3 Sub into (1), 3x2 + 2(41 + 4x)/3 + 1 = 0 9x2 + 82 + 8x + 3 = 0 9x2 + 8x + 85 = 0 Discriminant = 82 – 4(9)(85) < 0 There is no real soultion. (g） 3/(x - 1) + (x+1)/( x+3) = 8/(x2 + 2x -3); x<>1 and x<>-3 [3(x+3) + (x-1)(x+1)] / (x -1)(x+3) = 8/(x2 + 2x -3) 3x + 9 + x2 – 1 = 8 3x + x2 = 0 x(3 + x) = 0 x = 0 or x = -3 (rejected) (h) x + 2x/(x - 3) = 6/(x – 3); x<>3 x(x – 3) + 2x = 6 x2 – 3x + 2x – 6 = 0 x2 – x – 6 = 0 (x – 3)(x + 2) = 0 x = -2 or x = 3 (rejected)
其他解答:
MATHS(解方程)
發問:
1. 解以下方程。 如有需要 , 答案準至3位有效數字(a) x^4 - 3x^2 - 4 = 0(b) x - 4/x = 2(c) √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) 顯示更多 1. 解以下方程。 如有需要 , 答案準至3位有效數字 (a) x^4 - 3x^2 - 4 = 0 (b) x - 4/x = 2 (c) √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)
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最佳解答:(a) x4 - 3x2 - 4 = 0 (x2 – 4)(x2 + 1) = 0 (x – 2)(x + 2)(x2 + 1) = 0 x = 2 or x = -2 (b) x - 4/x = 2; x<>0 x2 – 4 = 2x x2 – 2x – 4 = 0 x = {2 +/-√ [22 + 4(1)(4)]}/2 x = 1 +/-√ 5 x = 3.24 or x = -1.24 (c) √(x - 1) = x - 3 x – 1 = (x – 3)2 x – 1 = x2 – 6x + 9 x2 – 7x + 10 = 0 (x – 2)(x – 5) = 0 x = 5 or x = 2 (rejected) since √1 <> -1 (d) (x + 1)2 - 4(x + 1) - 5 = 0 Let u = x + 1 u2 – 4 u – 5 = 0 (u – 5)(u + 1) = 0 u = 5 => x = 4 or u = -1 => x = -2 (e) { y = x2 - 2x – 3 … (1) { x + y - 3 = 0 … (2) Sub (1) into (2) x + x2 - 2x – 3 – 3 = 0 x2 – x – 6 = 0 (x – 3)(x + 2) = 0 x = 3 => y = 0 or x = -2 => y = 5 (f) {3x2+ 2y + 1 = 0 … (1) {3y - 4x = 41 y = (41 + 4x)/3 Sub into (1), 3x2 + 2(41 + 4x)/3 + 1 = 0 9x2 + 82 + 8x + 3 = 0 9x2 + 8x + 85 = 0 Discriminant = 82 – 4(9)(85) < 0 There is no real soultion. (g） 3/(x - 1) + (x+1)/( x+3) = 8/(x2 + 2x -3); x<>1 and x<>-3 [3(x+3) + (x-1)(x+1)] / (x -1)(x+3) = 8/(x2 + 2x -3) 3x + 9 + x2 – 1 = 8 3x + x2 = 0 x(3 + x) = 0 x = 0 or x = -3 (rejected) (h) x + 2x/(x - 3) = 6/(x – 3); x<>3 x(x – 3) + 2x = 6 x2 – 3x + 2x – 6 = 0 x2 – x – 6 = 0 (x – 3)(x + 2) = 0 x = -2 or x = 3 (rejected)
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