Q11 - Problem using xy and x + y

Q.

Find \( x^2 + y^2 \) if \(x + y + xy = 15\) and \(x^2y + xy^2 = 56\) and both x,y are integers.

Solution:
Assume a = xy and b = x + y. You will get ab = 56 and a + b = 8 where a,b are both integers.
Only integers satisfying the above are 7,8.
If xy = 8, x + y = 7 there is no soltuion.
If x + y = 8, xy = 7, there is one solution pair: 1,7.
So \(x^2 + y^2 = 50\).

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