He probably graphed the equation and eyeballed the root as 13. This is an acceptable conjecture which can be proved by plugging in. A little fortuitious but... Then it is trival to prove that it is the only positive root.

You would deflate out the obvious root.

The discriminant of the right side is - 472, so 13 is the only positive root.

]]>If anyone's got a Good way to solve the above, please let me know!!:cool:]]>

x^3–(x+1)^2=2001

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