Question

The sum of a number and its reciprocal is $\frac{65}{8}$. Find the number

Answer 1

Let the number be 'x'

Since sum of a number and its reciprocal is $\frac{65}{8}$ so we have,

$x+\frac{1}{x}=\frac{65}{8}$

$8x^2+8=65x$

$8x^2-65x+8=0$

$8x^2-64x-x+8=0$

$8x(x-8)-1(x-8)=0$

$(8x-1)(x-8)=0$

$x=8,\frac{1}{8}$