Question

The sum of a number and its reciprocal is 10/3. Then the numbers are .​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{Let the number be }x$

$\implies \text{According to the question}$

       $x + \dfrac{1}{x} = \dfrac{10}{3}$

       $\text{Simplifying...}$

$\implies \dfrac{x^{2} + 1}{x} = \dfrac{10}{3}$

       $\text{Cross Multiplying...}$

$\implies 3x^{2} + 3 = 10x$

       $\text{Transposing }10x \text{ to L.H.S}$

$\implies 3x^{2} - 10x + 3 = 0$

       $\text{We can split }(-10x) \text{ as }(-9x-x)$

$\implies 3x^{2} - 9x - x + 3 = 0$

$\implies 3x(x-3) -1(x-3) = 0$

$\implies (x-3)(3x-1)=0$

$\implies \boxed{x = 3,\dfrac13}$