Question

The sum of a number and its reciprocal is one-eight of 34. What is the product of the number and its square root?

• A. $8$
• B. $32$
• C. $27$
• D. None of these

Answer 1

The correct option is A $8$

Let the number be $x$.

According to the question,

$x+\frac{1}{x}=\frac{34}{8}$

$\frac{x^2+1}{x}=\frac{17}{4}$

$4x^2+4=17x$

$4x^2-17x+4=0$

$4x^2-16x-x+4=0$

$4x(x-4)-1(x-4)=0$

$(x-4)(4x-1)=0$

$x=4,\frac{1}{4}$

Since,

$\Rightarrow 4\times \sqrt{4}$

$\Rightarrow 4\times 2$

$\Rightarrow 8$

Hence, this is the answer.