A quesion on establishment of nature of roots

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we are given an equation x5+x=10
. How to prove that the only root for the equation is irrational? I'm an average 12th standard student. So, please keep it low. Thanks in advance.
 
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Did you try using the Rational root Theorem?

It's quite clear that there is only one real root to the equation. If you can find a contradiction that the root cannot be rational, you are done :smile:
 
How to contradict? Assuming a p/q form doesn't help... the root must be of form non- terminating non-repeating decimal expansion... how to do that?
 
Akshay_Anti said:
How to contradict? Assuming a p/q form doesn't help... the root must be of form non- terminating non-repeating decimal expansion... how to do that?

The link Infinitum posted outlines the procedure. The rational zero theorem clearly describes all possible rational roots of the equation.
 

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