Math Olympiad Challenge | A Very Nice Algebra Poblem | X = ?

Sweden Math Olympiad Problem | A Very Nice Algebra Challenge
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[@user-zy1rw6yb9p]

Thanks

[@quigonkenny]

Starting from the option to go a+b = 5 a⁴+b⁴ = 97 to solve, I'll start from a+b = 5.
a + b = 5 ---- [1]
a⁴ + b⁴ = 97 ---- [2]
(a + b)² = 5²

[@marcosmoreiradossantos-tn7mx]

Questão bem elaborada e trabalhosa

[@abhinitkumar5826]

put the value and get the answer

[@mohammadazadi4535]

راه حل ساده تر وسریع تر از طریق تحلیلی بدست می آید در اعداد صحیح البته. ولی پاسخ جبری در اعدادحقیقی هم همان است.

[@reguedebulle]

If x=a^4 and a is not real. It can be possible than x is real for me.
For example if we have a=i so x=1 no? You see ? We cannot be sure than x is not real.
Si x=a^4 et que a est imaginaire. Il est possible que x soit réel pour moi.
Par exemple si a=i alors x=1 nan ? Vous voyez ? Ya pas de certitude que x ne soit pas réel.

[@comdo777]

asnwer=3 isit

[@anthony17mapoy46]

16 and 81