# eks plus one over eks...

Algebra Level 3

$x$ is a real number and $x+\frac{1}{x}=-\dfrac{7}{\sqrt{6}}$.

$[1]$. $\sin^{-1} (x+\frac{1}{x})$ is a real number.

$[2]$. $x^2+\frac{1}{x^2}=\frac{37}{6}$

$[3]$ The given information can not be true because by the AM-GM inequality, $x+\frac{1}{x}$ has to be greater than or equal to $2$. And $-\dfrac{7}{\sqrt{6}}$ is clearly less than $2$.

Which of these statements are correct?

This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.

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