<s>[INST] What is the value of $x^2 + y^2 + z^2$ if $x^2 y + y^2 z + z^2 x=2186$ and $xy^2 + y z^2 + z x^2=2188$ 
What is the value of $x^2 + y^2 + z^2$ if $x^2 y + y^2 z + z^2 x=2186$ and $xy^2 + y z^2 + z x^2=2188$, where $x,y,z$ are integers.  

My Attempt 
$(x^2 y + y^2 z + z^2 x) +(x^2 y + y^2 z + z^2 x) =2186+2188=4374$. 
From this we can derive $(x+y+z)(xy+yz+zx)-3xyz=4374$ . We can subtract the given equations to get $xy(x-y)+yz(y-z)+zx(z-x)=-2$. But after this , I can't figure out how to proceed.
Any help is appreciated. Thanks in advance.
 [/INST] $$\sum_{cyc}(x^2y-x^2z)=(x-y)(x-z)(y-z)=-2$$
and the rest for you.
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