Question

The difference between a natural number and twice its reciprocal is $\frac{47}{7}$, then the number is

• A. $2$
• B. $4$
• C. $8$
• D. $7$

Answer 1

The correct option is D $7$

Let the natural number be $x$
As per given conditions, we get
$x-\frac{2}{x}=\frac{47}{7}\Rightarrow \frac{x^2-2}{x}=\frac{47}{7}\Rightarrow 7x^2-14=47x\Rightarrow 7x^2-47x-14=0\Rightarrow 7x^2-49x+2x-14=0\Rightarrow 7x(x-7)+2(x-7)=0\Rightarrow (7x+2)(x-7)=0\Rightarrow x=-\frac{2}{7},7\therefore x=7(\because x\in N)$