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If m,n are the roots of the equation x^2...

If m,n are the roots of the equation `x^2 - x - 1 =0`, then the value of `(1 + m log_e 3 + ( m log_e 3)^2/2!+ ..... ) (1 + n log_e 3 + ( n log_e 3)^2/2!+ ..... )/(1 + mn log_e 3 + ( mn log_e 3)^2/2!+ ..... )` is equal to

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