Is the solution of the equation x

rs450nigglix2

rs450nigglix2

Answered question

2022-05-20

Is the solution of the equation x + arctan ( x ) = π irrational ?

Answer & Explanation

Hugo Bruce

Hugo Bruce

Beginner2022-05-21Added 10 answers

Yes. Let x be the solution to x + arctan ( x ) = π, then
arctan ( x ) = π x x = t a n ( π x ) x = t a n ( x ) .
Thus if x would be rational, also t a n ( x ) would be rational. This is impossible: You can use the statement you gave for showing that x + a r c t a n ( x ) = 1 is irrational.

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