A .Maths－百科全書

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A .Maths

發問:

A-B=10 A/B=A-B/A-B-2 A=??? 更新: A=???????????????

最佳解答:

The answer as follow, A-B=10-----------------------(1) A/B=(A-B)/(A-B-2)---------(2) From (2), A(A-B-2)=(A-B)(B) A2-AB-2A=AB-B2 A2-2AB+B2=2A (A-B)2=2A-------------------(3) sub (1) into (3) 102=2A 100=2A A=50 so 50-B=10 B=40 Proof: for (1) L.H.S. = 50-40 =10 =R.H.S. Proof: for (2) L.H.S. =50/40 =5/4 R.H.S. =(50-40)/(50-40-2) =10/8 =5/4 =L.H.S. so, A=50 , B=40

其他解答:

(A/B) = A - (B/A) - B - 2 = - (B/A) + 10 - 2 = - (B/A) + 8 Let x = B/A 1/x = - x + 8 1 = - x2 + 8x x2 - 8x + 1 = 0 x = {8±√[(-8)2 - 4(1)(1)]} /2 = {8±√60} /2 = 4±√15 B/A = 4±√15 B = (4±√15)A When B = (4+√15)A A - B = 10 A [1 - (4+√15)] = 10 A (-3 - √15) = 10 A = -10/(3 + √15) = -10 (3 - √15)/[(3 + √15)(3 - √15)] = -10 (3 - √15)/(-6) = 5(3 - √15)/3 When B = (4-√15)A A - B = 10 A [1 - (4-√15)] = 10 A (-3 + √15) = 10 A = 10/(-3 + √15) = 10 (-3 - √15)/[(-3 + √15)(-3 - √15)] = 10 (-3 - √15)/(-6) = 5(3 + √15)/3 2009-01-15 16:05:29 補充： A = 5(3 - √15)/3 or 5(3 + √15)/3