He function $f$ satisfies\[f(x) + f(2x + y) + 5xy = f(3x - y) + 2x^2 + 1\]for all real numbers $x$, $y$. determine the value of $f(10)$.

We have f(10) = -49.

Explanation:

We have

Putting x = 0 and y = 0 we get,

Now put x = 0 in the function equation we get

Hence the given function is an even function

Now put x = 2y in the functional equation we get

Now put y = x/2 we get

Thus f(10) equals

thus f(10) = -49

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