# "Nejprve hledáme nuly" #
# x ^ 5 + 3 x ^ 2 - x = x (x ^ 4 + 3 x - 1) #
# x ^ 4 + 3 x - 1 = (x ^ 2 + a x + b) (x ^ 2 - a x + c) #
# => b + c-a ^ 2 = 0, #
# "" a (c-b) = 3, #
# "" bc = -1 #
# => b + c = a ^ 2, "" c-b = 3 / a #
# => 2c = a ^ 2 + 3 / a, "" 2b = a ^ 2-3 / a #
# => 4bc = a ^ 4 - 9 / a ^ 2 = -4 #
# "Jméno k = a²" #
# "Pak dostaneme následující kubickou rovnici" #
# k ^ 3 + 4 k - 9 = 0 #
# "Náhradník k = r p:" #
# r ^ 3 p ^ 3 + 4 r p - 9 = 0 #
# => p ^ 3 + (4 / r ^ 2) p - 9 / r ^ 3 = 0 #
# "Zvolte r, takže 4 / r² = 3 => r =" 2 / sqrt (3) #
# "Pak dostaneme" #
# => p ^ 3 + 3 p - (27/8) sqrt (3) = 0 #
# "Náhradník p = t - 1 / t:" #
# => t ^ 3 - 1 / t ^ 3 - (27/8) sqrt (3) = 0 #
# => t ^ 6 - (27/8) sqrt (3) t ^ 3 - 1 = 0 #
# "Substitute u = t³, pak dostaneme kvadratickou rovnici" #
# => u ^ 2 - (27/8) sqrt (3) u - 1 = 0 #
#disc: 3 * (27/8) ^ 2 + 4 = 2443/64 #
# => u = ((27/8) sqrt (3) pm sqrt (2443) / 8) / 2 #
# => u = (27 sqrt (3) pm sqrt (2443) / 16 #
# "Vezměte řešení se znakem +:" # #
#u = 6.0120053 #
# => t = 1.8183317 #
# => p = 1.2683771 #
# => k = 1.4645957 #
# => a = 1.2102048 #
# => b = -0.50716177 #
# => c = 1.9717575 #
# x ^ 4 + 3 x - 1 = (x ^ 2 + a x + b) (x ^ 2 - a x + c) #
# "Takže kořeny jsou" #
#x = (-a pm sqrt (a ^ 2-4 * b)) / 2 #
# => x = -0.6051024 pm 0,93451094 #
# => x = -1,53961334 "NEBO" 0,32940854 #
#"A"#
#x = (a pm sqrt (a ^ 2-4 * c)) / 2 #
# => x = "není reálné jako" a ^ 2-4 * c <0 #
# "Takže máme tři nuly pro naši původní kvintickou rovnici:" #
#x = = -1,53961334 "NEBO" 0 "NEBO" 0.32940854 #
# "Koncové chování je" #
#lim_ {x -> - oo} = -oo "a" # #
#lim_ {x -> + oo} = + oo. "#
# "Takže máme" #
# -oo "………" -1.53961334 "………" 0 "………." 0.32940854 "…….. "+ oo #
#------0++++0----0+++++#
