Known x ²+ y ²＋ 2xy-2x-2y + 1 ≡ 0, find the 999 power of (x + y)

Known x ²+ y ²＋ 2xy-2x-2y + 1 ≡ 0, find the 999 power of (x + y)

x ²+ y ²＋ 2xy-2x-2y+1＝ （x+y)^2 -2(x+y)+1 = (x+y-1)^2 =0
So x + y = 1
So the answer you want is 1

(1) If | x-3 | + (y + 2) ²= 0, then the Y power of x =? (2) if | x | = 1, y ²= 9, and XY > 0, then x + 2Y =? (3) If 2x-y = 3 + y, then 2x-2y + 1 / X-Y =? Those who answer well will be highly praised!

(1)
It is known that | x-3 | + (y + 2) ^ 2 = 0
Because | x-3 |, (y + 2) ^ 2 are ≥ 0
Therefore, when their sum is zero, it must be zero at the same time
That is, x = 3, y = - 2
So, x ^ y = 3 ^ (- 2) = 1 / 9
(2)
|x|=1,y^2=9
So, x = ± 1, y = ± 3
Known XY > 0
So, x = 1, y = 3; Or x = - 1, y = - 3
So, x + 2Y = ± 7
(3)
2x-y=3+y
===> 2x-2y=3
===> x-y=3/2
Therefore: 2x-2y + 1 / X-Y = 2 (X-Y) + 1 / X-Y = 3 + (2 / 3) = 11 / 3

-2x ³ The 4th power of Y ÷ (- x) ² y ²） （-x）-（x-2y）（2y+x）+x（x-xy ²） Where x = - L, y = - 2

Take X and Y in and you can figure it out

Known, x-2y = 7, xy = - 5, then x ²+ 4y ²- 4=? If I understand, I won't get extra points until 9:30 All I know is that the result is 25

(x-2y) ²= x ²+ 4y ²- 4xy
49=x ²+ 4y ²+ twenty
x ²+ 4y ²= twenty-nine
x ²+ 4y ²- 4=25

Known x ²+ y ²- 2X + 4Y + 5 = 0, then (x + y) 2012 power = __

x ²+ y ²- 2x+4y+5=0
（x-1)^2+(y+2)^2=0
x=1,y=-2
(x+y)^2012=(1-2)^2012=1.

Known x ²+ y ²+ z ²- 2X + 4y-6z + 14 = 0, find the value of the 2013 power of the algebraic formula (X-Y-Z)

Known x ²+ y ²+ z ²- 2x+4y-6z+14=0,
(x-1) ²+ (y+2) ²+ (z-3) ²= 0
∴x-1=0;
x=1;
y+2=0;
y=-2;
z-3=0;
z=3;
Find the value of the 2013 power of the algebraic formula (X-Y-Z)
=(1+2-3)^2013
=0;
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