Solve the following quadratic equations by factorization method:
$x + \frac{1}{x} = \frac{26}{5}$

{5, \frac{1}{5}}

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{- 5, \frac{1}{5}}

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{5, \frac{- 1}{5}}

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None of these

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Solution

The correct option is A ${5, \frac{1}{5}}$
$x + \frac{1}{x} = \frac{26}{5}$
$\Rightarrow$ $5 x^{2} + 5 = 26 x$ [ Multiplying both sides by $5 x$ ]
$\Rightarrow$ $5 x^{2} - 26 x + 5 = 0$
$\Rightarrow$ $5 x^{2} - 25 x - x + 5 = 0$
$\Rightarrow$ $5 x (x - 5) - 1 (x - 5) = 0$
$\Rightarrow$ $(x - 5) (5 x - 1) = 0$
$\Rightarrow$ $x - 5 = 0$ and $5 x - 1 = 0$
$\Rightarrow$ $x = 5$ and $x = \frac{1}{5}$

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