1)

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


A) 8

B) 27

C) 32

D) 40

E) None of these

Answer:

Option A

Explanation:

Let the numbers be $x$.
Then, $x+\frac{1}{x}=\frac{34}{8}$
$\Leftrightarrow 8x^{2}-34x+8=0$
$\Leftrightarrow 4x^{2}-17x+4 = 0$
$\Leftrightarrow (4x-1)(x-4) = 0$
$\Leftrightarrow x =4$.
neglecting $x=\frac{1}{4},$ as x is a natural number.
$\therefore$ Required Number $=4 \times \sqrt{4}= 4 \times 2 = 8$.