eks plus one over eks...

Algebra Level 3

xx is a real number and x+1x=76x+\frac{1}{x}=-\dfrac{7}{\sqrt{6}}.

Read the following statements.

[1][1]. sin1(x+1x)\sin^{-1} (x+\frac{1}{x}) is a real number.

[2][2]. x2+1x2=376x^2+\frac{1}{x^2}=\frac{37}{6}

[3][3] The given information can not be true because by the AM-GM inequality, x+1xx+\frac{1}{x} has to be greater than or equal to 22. And 76-\dfrac{7}{\sqrt{6}} is clearly less than 22.

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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