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: 已知
: 1 1 1
: _ = _ + ---
: m n m+n
: 求
: n m
: _ + _ = ?
: m n
: 請大家幫我解答，謝謝

t=m/n,m=tn,m&n不為0

代入求解

1/(tn) = 1/n + 1/[(t+1)n]

1/t = 1 + [1/(t+1)]

1/[t(t+1)]=1

t^2+t-1=0

原式=t + (1/t)

= [(1-sqrt5)/2] + [2/(1-sqrt5)]

= [(1-sqrt5)/2] - [(1+sqrt5)/2]

= -sqrt5

同理

可算出另解為sqrt5...















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