All Questions
6 questions
1
vote
0
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47
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On a general system of linear equations in a derivative problem
For some days a problem that I encountered in the Calculus textbook of mine has been preying upon my mind. The problem is as follows:
Determine the expression for the polynomial $F(x)$ given that it ...
- 489
4
votes
3
answers
223
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Prove that $-\sqrt{c}<ab<0$ if $a^4-2019a=b^4-2019b=c$.
Let $a, b$ be two distinct real numbers and let $c$ be a positive real number such that
$a^4-2019a=b^4-2019b=c$.
Prove that $-\sqrt{c}<ab<0$.
I attempted to solve this question using calculus, ...
1
vote
1
answer
102
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How to solve a difficult system
Problem: solve in $\mathbb R^{3}$ this system
$$
\begin{cases}y(1+x+x^2+x^3)=\dfrac{z}{16}\\ y^2x(1+x+2x^2+x^3+x^4)=\dfrac{2z+17}{16}\\
y^3x^3(1+x+x^2+x^3)=\dfrac{z}{16}\\
y^4x^6=1
\end{cases}
$$
...
- 2,369
2
votes
1
answer
62
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Prove that, there no solution for $\left\{a_1,a_2,...,a_{16} \right\}\in \mathbb{R} $
Prove that, there no solution
$$\begin{cases}
a_1^2+a_2^2+a_3^2+...+a_{16}^2=2017\\
a_1+a_2+a_3+...+a_{16}=1009\\
\end{cases}$$
for $\left\{a_1,a_2,...,a_{16} \right\}\in \mathbb{R} $
I tried $...
- 506
1
vote
4
answers
211
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Solving a system of five polynomials
I am trying to solve the following system of equations for tuple $\left(a,b,c,d,t\right) \in \mathbb{R}^{4} \times [0,1]$, with parameter $\ell\in\mathbb{R}$.
$$
\begin{eqnarray}
a\frac{t^{2}}{2} - ...
- 1,153
3
votes
2
answers
144
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Solving $4y^4 - 4x^4 + x + y = 0$ (equation system of partial derivates)
I need help solving the following equation system:
$$ \frac{\partial}{\partial x} = 8xy + 4y^2 + \frac{y}{x^2 + y^2} = 0 $$
$$ \frac{\partial}{\partial y} = 8xy + 4x^2 - \frac{x}{x^2 + y^2} = 0 $$
I'...
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