Solve equation by factorization : x+1 x =2 1 20 - Vidyadip

Question

Solve equation by factorization : $x+\frac{1}{x}=2 \frac{1}{20}$

✓

Answer

$
\begin{aligned}
& x+\frac{1}{x}=2 \frac{1}{20} \\
& \Rightarrow 20 x^2+20=41 x \\
& \Rightarrow 20 x^2-41 x+20=0 \\
& \Rightarrow 20 x^2-16 x-25 x+20=0 \\
& \Rightarrow 4 x(5 x-4)-5(5 x-4)=0 \\
& \Rightarrow(5 x-4)(4 x-5)=0
\end{aligned}
$
Either $5 x-4=0$,
then $5 x =4$
$
\Rightarrow x =\frac{4}{5}
$
or
$
4 x-5=0 \text {, }
$
then $4 x=5$
$
\Rightarrow x =\frac{5}{4}
$
Hence $x=\frac{4}{5}, \frac{5}{4}$.

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