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Question 26

If $$\frac{x^2 - 1}{n^2 - 1} + \frac{2n^2(1 - x)}{n^4 - 1} = \frac{2x - 1}{1 - n^4} - \frac{1 - x}{1 + n^2}$$, then $$x = $$ ______.


Correct Answer: $$\large \frac{3}{4}$$

Solution

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TO BE FILLED - as printed the equation reduces to $$x^2(n^2 + 1) - 3x(n^2 - 1) + (2n^2 - 3) = 0$$, whose roots depend on $$n$$ and are not even real for $$n = 2$$, so the statement must be re-read from the paper before the answer is filled in.

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