Let 'x' and 'y' represent the integers.

The sum of x and y is 7:

x + y = 7

y = 7 - x

The sum of x^2 and y^2 is 25:

x^2 + y^2 = 25

Plug y = 7 - x into the above equation:

x^2 + (7 - x)^2 = 25

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click here to see the equation solved for x

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x1 = 4

x2 = 3

For x = 4 we have y = 7 - 4 = 3.

For x = 3 we have y = 7 - 3 = 4.

The two integers are 3 and 4.