Find the values of the integers x and y: 10x^(2)-90x+2xy+y^(2)+225=0

  (x, y) = (5, -5)

Step-by-step explanation:

The equation can be rewritten as ...

  9x^2 -90x +225 +x^2 +2xy +y^2 = 0

  9(x^2 -10x +25) +(x +y)^2 = 0

  9(x -5)^2 +(x +y)^2 = 0

The only way the sum of squares can be zero is for each square to be zero:

  x -5 = 0

  x +y = 0

Then x = 5 and y = -5.

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

70

step-by-step explanation: