Question

Solve:
$x+\frac{1}{x}=25\frac{1}{25}$

Answer 1

We have
$x+\frac{1}{x}=25\frac{1}{25}$

$\Rightarrow x+\frac{1}{x}=25+\frac{1}{25}\Rightarrow \frac{x^2+1}{x}=(25+\frac{1}{25})$

$\Rightarrow x^2+1=(25+\frac{1}{25})x\Rightarrow x^2-(25+\frac{1}{25})x+1=0\Rightarrow x^2-(25+\frac{1}{25})x+25\times \frac{1}{25}=0$

$\Rightarrow x^2-25x-\frac{1}{25}x+25\times \frac{1}{25}\Rightarrow (x^2-25x)-(\frac{x}{25}-25\times \frac{1}{25})=0\Rightarrow x(x-25)-\frac{1}{25}(x-25)=0$

$\Rightarrow (x-25)(x-\frac{1}{25})=0\Rightarrow x-25=0orx-\frac{1}{25}=0\Rightarrow x=25orx=\frac{1}{25}$