<s>[INST] $x^2-y^2=196$, can we find the value of $x^2+y^2$? $x$ and $y$ are positive integers. 
If $x^2-y^2=196$, can we know what the value of $x^2+y^2$ is?
Can anyone explain this to me? Thanks in advance.
 [/INST] $$
x^2-y^2=(x-y)(x+y)=14^2
$$
Since $(x+y)-(x-y)=2y$ either both $x+y$ and $x-y$ need to be even or both need to be odd. Since their product is even, both need to be even. There are two possible factorizations: $14\cdot14$ and $2\cdot98$. $14\cdot14$ implies $y=0$, so we want $x-y=2$ and $x+y=98$. That is, $x=50$ and $y=48$. Therefore,
$$
x^2+y^2=4804
$$
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