Question

The sum of a number and its reciprocal is $\frac{50}{7}$. Find the number.

Answer 1

let the number be $x$

Given that $x+\frac{1}{x}=\frac{50}{7}$

$\frac{x^2+1}{x}=\frac{50}{7}$

Cross multiplying we get

${7x}^2-50x+7=0$

$\Rightarrow {7x}^2-49x-x+7=0$

$\Rightarrow 7x(x-7)-(x-7)=0$

$\Rightarrow (7x-1)(x-7)=0$

so $x=7$ and $x=\frac{1}{7}$

Hence, the number is $7$