Question

A natural number, when added to its reciprocal gives a value which is one -- eighth of 34. Find is the product of the number and its square root?

• A. 8
• B. 27
• C. 32
• D. 45
• E. 28

Answer 1

The correct option is A

8

Let the number be x.

Then, $x+\frac{1}{x}=\frac{34}{8}\iff \frac{x^2+1}{x}=\frac{34}{8}\iff 8x^2-34x+8=0$ $\iff 4x^2-17x+4=0\iff \left(4x-1\right)\left(x-4\right)=0\iff x=4.$ $[neglectingx=\frac{1}{4},asxisanaturalno]$ $\therefore \mathrm{Re}quirednumber=4\times \sqrt{4}=4\times 2=8.$