Solving A Nice Math Algebra Problem | How to solve for variables "a "and "b"? | Geendle

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In this Vídeo I solve this symultaneous equations a+b=4; a^5 + b^5 =464
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[@theupson]

because f(a,b) = f(b,a), i started by using a = 2+ x, b=2 -x ... solutions for x will be in equal and opposite pairs, and this substitution into the second given will result in a quartic. that quartic must have factors of the form (c - x^2) only because of the first observation, meaning it is really quadratic in x^2.
distributing and combining (2+x)^5 + (2-x)^5 is demeaning and time-consuming, but is most of the work in the problem.