The number of roots of the equation, .

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

The number of roots of the equation, ((x−1)(x−3)(x−2)(x−4))x−ex((x+1)(x+3)(x+2)(x+4))x=0\left( \frac{(x-1)(x-3)}{(x-2)(x-4)} \right)^x - e^x \left( \frac{(x+1)(x+3)}{(x+2)(x+4)} \right)^x = 0 .

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