# Tagged Questions

This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

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### Product of uncommon real roots?

The product of uncommon real roots of the two polynomials $p(x)=x^4+2x^3-8x^2-6x+15$ And $q(x)=x^3+4x^2-x-10$ My attempt was to form an equation of form $p(x)+\lambda q(x)=0$ ...
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### System of two quadratic equations in two variables with two parameters leads to quintic polynomial

Actually, it's two closely related systems. Let $a,b \in \mathbb{Q}$ be the parameters. The first system has the form: $$(1+a y)x^2-2(a+y)x+(1+a y)=0 \\ (1-b x)y^2-2(b-x)y+(1-b x)=0$$ One of the ...
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### Find a least upper bound for $3^{x+y-4}+(x+y+1)2^{7-x-y}-3(x^2+y^2)$ with some constraint?

This is a question in vietnamese national math exam at the end of 12th grade. Given x,y are real numbers which satisfy the condition: $x+y+1=2(\sqrt{x-2}+\sqrt{y+3})$ Find a $m$ such that: ...
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### Closed-form formula for system of two bivariate quadratic polynomials

Given a system of two bivariate quadratic polynomials: \begin{eqnarray} a_0 + a_1 x + a_2 y + a_3 xy+a_4 x^2 + a_5 y^2 &= 0 \\ b_0 + b_1 x + b_2 y + b_3 xy+b_4 x^2 + b_5 y^2 &= 0 \end{...
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\begin{align} ax+y+z&=1,\\ 2x+2ay+2z&=3\\ x+y+az&=1 \end{align} I tried forming the system matrix and discuss it using its rank, but I'm not sure how to row reduce: $$\begin{pmatrix}a&... 0answers 36 views ### What is the difference between an autonomous system and a dynamical system? Wikipedia says, Autonomous systems are closely related to dynamical systems. Any autonomous system can be transformed into a dynamical system and, using very weak assumptions, a dynamical system ... 0answers 38 views ### Solution to a non linear system of equations Does there exist an interval I such that this system of equations has no solution? ... 2answers 52 views ### Solve three equations for three unknowns. [duplicate] So I have the following three equations which I do not know how to solve: -D * x - E * y = A + (R * D) E * F * x - D * F * y - G * z = B - (R * E * F) E * G * x - D * G * y + F * z = C - (R * E * G)... 2answers 57 views ### Value of z in the given system of equations If$$\{x\}+y+\lfloor{z}\rfloor=3.1x+\lfloor{y}\rfloor+\{z\}=2.4\lfloor{x}\rfloor+\{y\}+z=1.3$$then find the value of z. My attempt: I converted fractional part of every equation to ... 0answers 29 views ### Workability of linear equation solving methods for different fields? So far, I have mostly done linear algebra over \mathbb R and \mathbb{C}. I know there exist very many methods to solve equation systems for those fields, of which a few are Gaussian Elimination, ... 3answers 35 views ### System of Equation Solve the system of equations$$-x_1+x_2+x_3=ax_1-x_2+x_3=bx_1+x_2-x_3=c$$I have tried writing the augmented matrix of the system of equations above and reducing it into echelon form ... 0answers 11 views ### An algorithm to find the general classical solution to a linear gradient system in partial derivatives I'm looking for a book where the algorithm to construct the general solution for system$$\nabla u(x,y) = \vec a(x,y)\cdot \nabla v(x,y)$$is given. Could ypu please advice me some source? 2answers 82 views ### Why can the equation Ax = b not be solved for every b Let A be a 3 \times 2 matrix . Explain why the equation A\vec{x} = \vec{b} cannot be solved for every \vec{b} in \mathbb{R}^3. What about a 4 \times 3 matrix? I'm not sure how to answer ... 0answers 30 views ### Solving a system of N-1 Ist order ODEs by Euler's Method In order to solve a system of N-1 first order ODEs by Euler's Method For N = 4; t=0, h= 0.1, x= 0.1 should the Euler formula be? U_n(t+h) = U_n(t) + h F_n(x_n, t_n) for n = 1, 2,..,N-1 but we ... 2answers 44 views ### What can be a good programming algorithm to solve the given equation other than the brute force? [closed] Find all x, y and z for n=100;$$x^2 + y^2 + z^2 = n$$x,\ y, and z should be positive integers. 2answers 24 views ### Simultaneous recurrence relations Currently working on solving this set of three simultaneous recurrences, but having some trouble. Tried various substitutions, but still cannot seem to make any progress. Also, none of the three ... 3answers 159 views ### A System of Infinite Linear Equations Suppose that \{a_{i}\}_{i=-\infty}^{\infty} with \sum_{i=-\infty}^\infty a_{i} \lt \infty is known and that \{b_i\}_{i=-\infty}^{\infty} is such that$$\sum_{i=-\infty}^\infty a_{i}b_{-i} =1,$$... 4answers 47 views ### Symmetric system of 3 equations I need help solving the following system for all real ordered triples (x,y,z) without guessing and checking:$$x+y+z=23xy+yz+xz=144xyz=252$$Preferably, the solution should use methods ... 1answer 48 views ### Solving a system of non linear equations I have got a system of non-linear equations of the form$$A x_1^B \exp \bigg(\frac{- C}{x_1} \bigg) = k_1A x_2^B \exp \bigg(\frac{- C}{x_2} \bigg) = k_2A x_3^B \exp \bigg(\frac{- C}{x_3} \...
I have a probably very simple problem here. A system of nonlinear equations. \left\{ \begin{align} & {{x}^{2}}+{{y}^{2}}=26 \\ & x+{{y}^{2}}=6 \\ \end{align} \right. I started with ...