Question

If the sum of a natural number and its reciprocal is $\frac{50}{7}$, then the number is

Answer 1

Let the natural number be $x$ and
$x+\frac{1}{x}=\frac{50}{7}\Rightarrow 7x^2-50x+7=0\Rightarrow 7x^2-49x-x+7=0\Rightarrow 7x(x-7)-1(x-7)=0\Rightarrow (x-7)(7x-1)=0\Rightarrow x=\frac{1}{7},7\therefore x=7(\because x\in N)$