Given X3 + x2 + X + 1 = 0, find the value of 1 + X + x2 + X3 + X4

Given X3 + x2 + X + 1 = 0, find the value of 1 + X + x2 + X3 + X4

1 + X + x2 + X3 + X4 = 1 + X (X3 + x2 + X + 1), and ∵ X3 + x2 + X + 1 = 0, the original formula = 1 + X × 0 = 1

X2-13x + 1 = 0, what is the value of x2 + 1 / x2?
X2 is the square of X

Divide both sides of x2-13x + 1 = 0 by X to get x + 1 / x = 13. Square both sides of X + 1 / x = 13 to get x2 + 1 / x2 + 2 = 169, so x2 + 1 / x2 = 169-2 = 167

Solving inequality: X3 + x2-12x less than 0
The third power of x plus the square of x minus 12x is less than 0

x^3+x^2-12