The absolute value of No a-1 plus the square of the sum of b+2=0 is the value of the sum of a plus b to the power of 2010 plus the power of 2009. Shortly,

The absolute value of No a-1 plus the square of the sum of b+2=0 is the value of the sum of a plus b to the power of 2010 plus the power of 2009. Shortly,

| A-1(b+2)2=0
The absolute value and that complete square are non-negative,
So a-1=0, b+2=0
So a=1, b=-2
(A+b)^2010+a^2009
=(-1)^2010+1^2009
=1+1
=2

If the absolute value of the square of (x+1)+1)=0. Then the 2008 power of x + the 2009 power of y =____

Square of (x+1)+ absolute value of y-1=0
And the square of (x+1)≥0, the absolute value of y-1≥0
Square of (X+1)=0, absolute value of y-1=0
I.e. x=-1, y=1
X's 2008 power +y's 2009 power =(-1)'s 2008 power +1's 2009 power =1+1=2