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.