Given the square of x+x+1=0, find the 2006 power of x+x and the 2005 power of x+x and the 2004 power of x +…… Square of x + value of x+1

Given the square of x+x+1=0, find the 2006 power of x+x and the 2005 power of x+x and the 2004 power of x +…… Square of x + value of x+1

The result is 0
Because x's 2006 power +x's 2005 power +x's 2004 power +…… The number of 2007 in the middle of x+x+1 is a multiple of 3, that is, every three is a group of e.g. x's 2006 power +x's 2005 power +x's 2004 power = x's 2004 power (x's square +x+1)=0
By analogy, there are 669 0s in total, so the result is 0

Calculate the 2001 power of (-2)+ the 2002 power of (-2)

(-2)^2002=(-2)*(-2)^2001
Therefore, the original formula =(-2)^2001*(1+(-2))=-(-2)^2001=2^2001