Chapter: Quadratic Equations· Mathematics Part 1 (Algebra)
Answer: The number is 5
Let the number be \(x\). \(x + \dfrac{1}{x} = \dfrac{26}{5}\)
\(5x^2 + 5 = 26x \Rightarrow 5x^2 - 26x + 5 = 0\)
\(5x^2 - 25x - x + 5 = 0 \Rightarrow 5x(x - 5) - 1(x - 5) = 0\)
\((x - 5)(5x - 1) = 0 \Rightarrow x = 5\) or \(x = \dfrac{1}{5}\)
A natural number is required, so \(x = 5\). Check: \(5 + \dfrac{1}{5} = \dfrac{26}{5}\) ✓.