The sum of a number and its reciprocal is
Question:

The sum of a number and its reciprocal is $2 \frac{1}{20}$. The number is

(a) $\frac{5}{4}$ or $\frac{4}{5}$

(b) $\frac{4}{3}$ or $\frac{3}{4}$

(c) $\frac{5}{6}$ or $\frac{6}{5}$

(d) $\frac{1}{6}$ or 6

 

Solution:

(a) $\frac{5}{4}$ or $\frac{4}{5}$

Let the required number be $x$.

According to the question:

$x+\frac{1}{x}=\frac{41}{20}$

$\Rightarrow \frac{x^{2}+1}{x}=\frac{41}{20}$

$\Rightarrow 20 x^{2}-41 x+20=0$

$\Rightarrow 20 x^{2}-25 x-16 x+20=0$

$\Rightarrow 5 x(4 x-5)-4(4 x-5)=0$

$\Rightarrow(4 x-5)(5 x-4)=0$

$\Rightarrow x=\frac{5}{4}$ or $x=\frac{4}{5}$

 

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