JAMB - Mathematics (1993 - No. 13)
Evaluate (x + \(\frac{1}{x}\) + 1)2 - (x + \(\frac{1}{x}\) + 1)2
4x2
(\(\frac{2}{x}\) + 2)2
4
4(1 + x)
Explanation
(x + \(\frac{1}{x}\) + 1)2 - (x + \(\frac{1}{x}\) + 1)2
= (x + \(\frac{1}{x}\) + 1 + x + \(\frac{-1}{x}\) - 1)(x - \(\frac{1}{x}\) + 1 - x + \(\frac{1}{x}\) + 1)
= (2x) (2 + \(\frac{2}{x}\)) = 2x x 2(1 + \(\frac{1}{x}\))
4x (1 + \(\frac{1}{x}\)) = 4x + 4
= 4(1 + x)
= (x + \(\frac{1}{x}\) + 1 + x + \(\frac{-1}{x}\) - 1)(x - \(\frac{1}{x}\) + 1 - x + \(\frac{1}{x}\) + 1)
= (2x) (2 + \(\frac{2}{x}\)) = 2x x 2(1 + \(\frac{1}{x}\))
4x (1 + \(\frac{1}{x}\)) = 4x + 4
= 4(1 + x)
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