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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