Prove that the only real root of the equation$\displaystyle x^7-14x^6+21x^5-70x^4+35x^3-42x^2+7x-2=0$ is .
Well, the easy way out is to graph it, showing that there is only one real solution, then plug the target value of x into the equation and verify that it is a solution. (It'll be a real monster of an expansion, I'm sure! )
But that's probably not what you are looking for.
-Dan