Carcass wrote:

If x > o and the quantities \(\sqrt{x}\) and \(\frac{\sqrt{x}}{x}\) are reciprocals, which of the following

could be true?

Indicate

all choices that apply.

❑ \(\sqrt{x}\) is greater than \(\frac{\sqrt{x}}{x}\)

❑ \(\sqrt{x}\) is less than \(\frac{\sqrt{x}}{x}\)

❑ \(\sqrt{x}\) is greater than \(x\)

Given x>0 but it has not mentioned x is integer or fraction

Let consider x = 4

now \(\sqrt{4}\) and \(\frac{\sqrt{4}}{4}\)

or 2 > \(\frac{1}{2}\) - This staisfy 1st equation and also they are reciprocal.

Now let conside x = \(\frac{1}{4}\)

Therefore \(\sqrt{x}\) and \(\frac{\sqrt{x}}{x}\)

\(\sqrt{\frac{1}{4}}\) and \(\frac{\sqrt{\frac{1}{4}}}{\frac{1}{4}}\)

= \(\frac{1}{2}\) and \(\frac{1}{2} *4\)

= 1/2 and 2

i.e \(\frac{1}{2}\)< 2 so this satisfy the second equation i.e\(\sqrt{x}\) is less than\(\frac{\sqrt{x}}{x}\)

Now if we consider again x= 1/4

Then \(\sqrt{x}\) and \(x\)

= \(\sqrt{\frac{1}{4}}\) and \(\frac{1}{4}\)

= \(\frac{1}{2}\) > \(\frac{1}{4}\) - This satidfy our third equation.

Hence A,B,C are all correct

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