Nullstellen: x^5 - 41·x^3 + 400·x = 0

Question

Hi

Term: x^5 - 41·x^3 + 400·x = 0

lautet der Ansatz

x²*(x³-41x+400) = 0

oder

x*(x⁴-41x²+400) = 0

Gruß

Answer 1

x^5 - 41·x^3 + 400·x = x·(x^4 - 41·x^2 + 400) = 0

x₁ = 0

x^4 - 41·x^2 + 400 = 0

z^2 - 41·z + 400 = 0

z = 25 ∨ z = 16

x_2/3 = ± 5

x_4/5 = ± 4