Solve :
`(3x + 2y - 7)^(2) + (5x + 7y - 13)^(2) = 0`, for real values of x and y.

Explanation

We have `(3x + 2y - 7)^(2) + (5x + 7y - 13)^(2) = 0`
Since squares of real numbers are always greater than or equal to zero. So, sum of squares of two real numbers will also be greater than or equal to zero and sum of squres of two real numbers are zero only when both numbers are zero.
`therefore 3x + 2y - 7 = 0`....(1)
and 5x + 7y - 13 = 0 ....(2)
Solving equations (1) and (2), we get
`x = (23)/(11) , y = (4)/(11)`.