![(x−y)=13and \: xy=−5find \: \: value \: of \: \frac{1}{3} ( {x}^{2} + {y}^{2} )\ \textless \ br /\ \textgreater \](https://tex.z-dn.net/?f=%28x%E2%88%92y%29%3D13and+%5C%3A+xy%3D%E2%88%925find+%5C%3A++%5C%3A+value+%5C%3A+of+%5C%3A++%5Cfrac%7B1%7D%7B3%7D+%28+%7Bx%7D%5E%7B2%7D+%2B++%7By%7D%5E%7B2%7D++%29%5C++%5Ctextless+%5C+br+%2F%5C++%5Ctextgreater+%5C+ "(x−y)=13and \: xy=−5find \: \: value \: of \: \frac{1}{3} ( {x}^{2} + {y}^{2} )\ \textless \ br /\ \textgreater \")
solve it please
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Answer:
As we know that
(x-y)^2= x^2+y^2-2xy
13^2=x^2+y^2-2×-5
169-10=x^2+y^2
159= x^2+y^2
Now, 1/3×159
= 53
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