Question

Plz tell to solve x+1/x=2.5 using factorization method (quadataric eqn.)

Answer 1

$x + \frac{1}{x} = \frac{25}{10} \\ \frac{ {x}^{2} + 1 }{x} = \frac{25}{10} \\ 10 {x}^{2} + 10 = 25x \\ 10 {x}^{2} - 25x + 10 = 0 \\ 1 0 {x}^{2} - 20x - 5x + 10 = 0 \\ 10x(x - 2) - 5(x - 2) = 0 \\( 10x - 5)(x - 2) = 0 \\ 10x = 5 \\ x = \frac{5}{10} \\ x = \frac{1}{2} \\ \\ x - 2 = 0 \\ x = 2$