Question

The sum of a number and its reciprocal is $17/4$. The number is ____________.

• A. $5$
• B. $4$
• C. $6$
• D. $3$

Answer 1

Answer: (B)

$4$

Let the number be $x$

Given Sum of a number and its reciprocal is $17/4$

$⟹x+\frac{1}{x}=\frac{17}{4}$

$⟹\frac{x^2+1}{x}=\frac{17}{4}$

$⟹4x^2+4=17x$

$⟹4x^2-16x-x+4=0$

$⟹4x(x-4)-(x-4)=0$

$⟹(4x-1)(x-4)=0$

$⟹x=\frac{1}{4},4$

So the number is $4$