Answer Very Carefully!

Algebra Level 4

Which of the following statements is/are correct?

[1][1] An irrational number times a rational number is always an irrational number.

[2][2] The statement tan1x+tan1y=tan1(x+y1xy)\tan^{-1} x + \tan^{-1} y=\tan^{-1}\left( \frac{x+y}{1-xy}\right) is true for all real numbers xx and yy.

[3][3] If xy=yxx^y=y^x, then x=yx=y where xx and yy are positive real numbers.


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