The sum of a number and its reciprocal is 5.2. The number is

1. 5 or $\dfrac{1}{5}$

2. 2 or $\dfrac{1}{2}$

3. 4 or $\dfrac{1}{4}$

4. -2 or $-\dfrac{1}{2}$

Let number be x.

Given,

Sum of a number and its reciprocal is 5.2

$\Rightarrow x + \dfrac{1}{x} = 5.2 \\[1em] \Rightarrow \dfrac{x^2 + 1}{x} = \dfrac{52}{10} \\[1em] \Rightarrow 10(x^2 + 1) = 52x \\[1em] \Rightarrow 10x^2 + 10 = 52x \\[1em] \Rightarrow 10x^2 - 52x + 10 = 0 \\[1em] \Rightarrow 10x^2 - 50x - 2x + 10 = 0 \\[1em] \Rightarrow 10x(x - 5) - 2(x - 5) = 0 \\[1em] \Rightarrow (10x - 2)(x - 5) = 0 \\[1em] \Rightarrow 10x - 2 = 0 \text{ or } x - 5 = 0 \\[1em] \Rightarrow 10x = 2 \text{ or } x = 5 \\[1em] \Rightarrow x = \dfrac{2}{10} \text{ or } x = 5 \\[1em] \Rightarrow x = \dfrac{1}{5} \text{ or } x = 5.$

Hence, Option 1 is the correct option.