- CRebeccaLv 69 years agoFavorite Answer
f(x)=x^5 is continuous function.(連續函數)
f(0) <2011, f(5) > 2011, so there exists k in (0,5), f(k)=2011
(Note: k is positive number(正數).)
f(x)=x^5 is increasing function. (漸增函數)
If a < b and a, b both are solutions of x^5=2011 then a^5=b^5=2011.
But a^5 < b^5 (since x^5 is increasing) contradicts to a^5=b^5,
so that it is impossible to find two different solutions of x^5=2011.