Given x ^ 2 + x = - 1, find the value of x ^ 2009 + x ^ 2008 +. + x ^ 2 + X + 1 | Math enthusiast | Mathematical art

Given x ^ 2 + x = - 1, find the value of x ^ 2009 + x ^ 2008 +. + x ^ 2 + X + 1

That is, x ^ 2 + X + 1 = 0
Every three in the back
Original formula = x ^ 2007 (x ^ 2 + X + 1) + x ^ 2004 (x ^ 2 + X + 1) + +(x^2+x+1)
=0+0+…… +0
=0

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