Is this : <msqrt> 3 + <msqrt> 2 + <msqrt> 3

Erin Lozano

Erin Lozano

Answered question

2022-06-05

Is this : 3 + 2 + 3 + 2 + irrational number?

Answer & Explanation

Ryan Fitzgerald

Ryan Fitzgerald

Beginner2022-06-06Added 17 answers

As soon as you are sure that such expression makes sense, it is a root of ( x 2 3 ) 2 2 x = x 4 6 x 2 x + 7 which does not have any rational root.
Jasmin Pineda

Jasmin Pineda

Beginner2022-06-07Added 2 answers

As Masacroso has already pointed out in the comments, you have to find rational solutions to
c = 3 + 2 + c
c 2 = 3 + 2 + c
c 2 3 = 2 + c
( c 2 3 ) 2 = 2 + c
c 4 6 c 2 + 9 = 2 + c
So the answer to your question is whether there are any rational solutions to c 4 6 c 2 c + 7 = 0 or not. Actually not.

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