Нужно решить уравнение x¹⁰+31x⁵-32=0

X^10 - 31x^5 - 32 = 0
t = x^5

t^2 - 31t - 32 = 0
D = 961 + 128 = 1089 = 33^2

t1 = (31+33)/2 = 32
t2 = (31-33)/2 = -1

x^5 = 32
x = 2

x^5 = -1
х = -1

ответ: -1 и 2