(1) Given the square of x + x +1=0, find the 2012 power of x + the 2011 power of x +…… +X squared +x+1 (2) Given that x is not equal to y, and the square of x-x=2, the square of y-y=2, find the value of the square of the algebraic expression x-xy+y

(1) Given the square of x + x +1=0, find the 2012 power of x + the 2011 power of x +…… +X squared +x+1 (2) Given that x is not equal to y, and the square of x-x=2, the square of y-y=2, find the value of the square of the algebraic expression x-xy+y

(1) Because the square of x + x +1=0, the 2012 power of x + the 2011 power of x +…… +X squared +x+1
=2010 Power of X (square of x+x+1)+2007 power of X (square of x+x+1)+2004 power of X (square of x+x+1)+... +X (square of x +x+1)+1=1
(2) The square of x-x=2, the square of y-y=2, so x, y is the root of the square of equation t-t=2, because x is not equal to y, so x, y are two unequal real roots of this equation.
So x+y=1, xy=-2, so the square of x-xy+y=(x+y) the square of -3xy=7

Given the square of x + x +1=0, find the 2012 power of x + the 2011 power of x +…… +X squared +x+1 Lesson Multiplication Formula Lesson

2012 Power of x +2011 power of x +…… +X squared +x+1
Start from scratch and split into groups of three
(X to 2012+ x to 2011+ x to 2010)+... +(Square of x +x+1)
=2010 Power of x (square of x+x+1)+2007 power of x (square of x+x+1)+... +(Square of x +x+1)
=0
Each group is 0