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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?
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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?
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Dec
27
revised How to solve an irrational equation?
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