Question

solve for x x plus 1/ x = 5/2​

Answer 1

$Given \:x + \frac{1}{x} = \frac{5}{2}$

$\implies \frac{x^{2} + 1 }{x} = \frac{5}{2}$

$\implies 2(x^{2} + 1 ) = 5x$

$\implies 2x^{2} - 5x + 2 = 0$

/* Splitting the middle term,we get */

$\implies 2x^{2} - 4x - 1x + 2 = 0$

$\implies 2x( x - 2) - 1( x - 2 ) = 0$

$\implies (x-2)(2x-1) = 0$

$\implies x - 2 = 0 \:Or \: 2x - 1 = 0$

$\implies x = 2 \:Or \: x = \frac{1}{2}$

Therefore.,

$\green {x = 2 \:Or \: x = \frac{1}{2}}$

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