Question

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

Answer 1

Given,
X + 1 / X = 34 / 8
$= > x + \frac{1}{x} = \frac{34}{8} \\ = > 8{x}^{2} + 8 = 34x \\ = > 4 {x}^{2} + 4 = 17x \\ = > 4 {x}^{2} - 17x + 4 = 0 \\ \\ by \: solving \: it \: \\ x = \frac{1}{4} \: or \: 4.$
Now we have to find,
$x + \sqrt{x} = 4 + 2 \: \: or \: \: \frac{1}{4} + \frac{1}{2} \\ = > x + \sqrt{x} = 6 \: \: or \: \: \frac{3}{4}.$
Hope this will help you.

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