Quintic Equation #math #maths

#brainexercise #matholympics
Quintic Equation

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[alexandregaeng]

Found a funny equality with a = 362 and b = a²-1=131043, we get polynomial x^5-5(x^3)+5x-724 which has x = 4 as root, but with the generalized formula by unicity of root on R+ with function variations we get ;)

[alexandregaeng]

Joke apart I found non trivial solution by binomial expansion and generalized the example. If a in Z, b in N and a^2-b = 1, then x = is a solution of x^5-5(x^3)+5x-2a=0. For example if a = 5 and b = 24, x = is a solution of x^5-5(x^3)+5x-10=0

[alexandregaeng]

Or quick solution: f(x) = 0 = 0+0x+0x² lol.