minthao_2011
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 Apr 10 revised How can I prove the equation has unique positive real solution? added 195 characters in body Apr 10 asked How can I prove the equation has unique positive real solution? Apr 3 awarded Nice Answer Mar 10 comment How can I prove this equation has no solution? \begin{align*} x^5-x^4-x^3-3x^2+x-1&=x^5-x^3-2x^2-(x^2-x+1)-x^4\\ & =x^2 (x^3-x-2)-(x^2-x+1)-x^4 \end{align*} From the given equation, we have $x^3-x-2 \leqslant 0.$ Another way $x^2-x+1 >0$ and $x^4 \geqslant 0.$ Therefore $$x^5-x^4-x^3-3x^2+x-1< 0.$$ Mar 10 comment How can I prove this equation has no solution? Thank you very much. You have a good idea. I change by $g(x) = \dfrac{1}{2}(3x+1)$. And a new prolem is if $x\in (0,1)$, we have not yet prove the equation has no solution. Please try again. Mar 10 comment How can I prove this equation has no solution? your link is problem equation has no rational solution. Mar 10 comment How can I prove this equation has no solution? Note that, every an odd polynomial always has solution. Therefore, I think, we must use the condition $-x^3 + x + 2 \geqslant 0$. But, now I can not. Mar 10 comment How can I prove this equation has no solution? I think It is not simple. Can you prove it? Mar 10 comment How can I prove this equation has no solution? How can I prove the equation $x^5-x^4-x^3-3 x^2+x-1=0$ has no solution? Mar 10 comment How can I prove this equation has no solution? @imranfat Using graph is not a solution. Mar 9 comment How can I prove this equation has no solution? OK. It is not simple $(x+1) \left(x^5-x^4-x^3-3 x^2+x-1\right)=0$ Mar 9 comment How can I prove this equation has no solution? @Deepak Please see the last equation in my tried. Mar 9 asked How can I prove this equation has no solution? Feb 25 comment Is there another way to solve this equation? I think, this is not a solution. Feb 25 revised Is there another way to solve this equation? added 13 characters in body Feb 25 asked Is there another way to solve this equation? Jan 13 awarded Popular Question Dec 29 answered Complex numbers equation: $z^4 = -16$ Dec 27 revised How to solve an irrational equation? edited body Dec 27 revised How to solve an irrational equation? edited body