Betcha you can't solve this?...

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Let f(x) be:

$f(x) = (\overline{x} + a)(\overline{x} + b)...(\overline{x} + z)$ ,

that said f(x) can also be expressed as:

( $\overline{x}$ is the addtive inverse of x)

\overline{x}^{26} - a^{26} - ... - z^{26}

x^{26} - a^{26} - ... - z^{26}

x-\overline{x}

1 solution

Test User
Mar 10, 2014

This is a very clever problem. The solution lies in the fact that one of the terms is $(\overline{x} - x)$ which is equal to 0, therefore the entire equation is equal to $\boxed{0}$ .

Yeah, you surely got it! But you made a little mistake by stating that one of the terms is $\overline{x} - x$ , while the correct is that one of the terms is $\overline{x} + x = -x + x$ , which equals to 0. But anyway, congratulations on solving the problem and sharing your solution to us!

Danilo Marques - 7 years, 3 months ago

Betcha you can't solve this?...

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