The first question: break down 34 into 25 and 9, and it becomes:

X^2+Y^2-6X+ 10Y+9+25=0

Changing the position is: (x 2-6x+9)+(y 2+ 10y+25) = 0.

If you change the formulas in the two brackets, you get: (x-3) 2+(y+5) 2 = 0, because the number obtained after squaring will not be negative, so you get X-3=0, Y+5=0, and the solution is: X=3, Y=-5, then X+Y=-2.

Question 2: multiply both sides of X-3Y= 1 by-1 to get 3Y-X=- 1, and bring it into the formula together with X-3Y. The original formula will be simplified to 7Y-2. Then, y=4/7 is obtained by solving two known conditions. Finally,

Question 3: If (-2) 2005 is regarded as an X, it can be simplified as: X+X *(2). If it is simplified, it is X-2X and becomes -X, then the result is -(-2) 2005. One more thing: the odd power of a negative number is still negative, so it is the same as the last one.

Note: 2 means square, and 2005 means 2005 power.