Question

Solve for x

$x + \frac{1}{x} = 25 \frac{1}{25}$
​

Answer 1

Step-by-step explanation:

Given:-

$\rm x + \dfrac{1}{x} = 25 \dfrac{1}{25}$

Solution:-

$\rm x + \dfrac{1}{x} = 25 \dfrac{1}{25}$

$\rm \dashrightarrow x + \dfrac{1}{x} = 25 + \dfrac{1}{25}$

$\rm \dashrightarrow \dfrac{ {x}^{2} + 1}{x} = 25 + \dfrac{1}{25}$

$\rm \dashrightarrow {x}^{2} + 1 = \bigg(25 + \dfrac{1}{25} \bigg)x$

$\rm \dashrightarrow {x}^{2} + 1 - \bigg(25 + \dfrac{1}{25} \bigg)x = 0$

$\rm \dashrightarrow {x}^{2} - 25x - \dfrac{1}{25} x + 25 \times \dfrac{1}{25} = 0$

$\rm \dashrightarrow ( {x}^{2} - 25x) - \bigg(\dfrac{x}{25} + 25 \times \dfrac{1}{25} \bigg) = 0$

$\rm \dashrightarrow x ( x - 25) -\dfrac{1}{25} (x - 25 ) = 0$

$\rm \dashrightarrow ( x - 25) \bigg(x - \dfrac{1}{25} \bigg) = 0$

$\rm \dashrightarrow ( x - 25) = 0 \: \: \: \: \: (or) \: \: \: \: x - \dfrac{1}{25} = 0$

$\boxed{ \leadsto\rm x = 25 \: \: or \: \: \dfrac{1}{25}}$