enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Extraneous and missing solutions - Wikipedia

    en.wikipedia.org/wiki/Extraneous_and_missing...

    Therefore, the solution = is extraneous and not valid, and the original equation has no solution. For this specific example, it could be recognized that (for the value x = − 2 {\displaystyle x=-2} ), the operation of multiplying by ( x − 2 ) ( x + 2 ) {\displaystyle (x-2)(x+2)} would be a multiplication by zero.

  3. Underdetermined system - Wikipedia

    en.wikipedia.org/wiki/Underdetermined_system

    An underdetermined linear system has either no solution or infinitely many solutions. For example, + + = + + = is an underdetermined system without any solution; any system of equations having no solution is said to be inconsistent. On the other hand, the system

  4. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  5. Fermat's Last Theorem - Wikipedia

    en.wikipedia.org/wiki/Fermat's_Last_Theorem

    In other words, it was necessary to prove only that the equation a n + b n = c n has no positive integer solutions (a, b, c) when n is an odd prime number. This follows because a solution (a, b, c) for a given n is equivalent to a solution for all the factors of n. For illustration, let n be factored into d and e, n = de. The general equation a ...

  6. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    In general, a system with fewer equations than unknowns has infinitely many solutions, but it may have no solution. Such a system is known as an underdetermined system. In general, a system with the same number of equations and unknowns has a single unique solution. In general, a system with more equations than unknowns has no solution.

  7. Overdetermined system - Wikipedia

    en.wikipedia.org/wiki/Overdetermined_system

    For M ≥ N, there may be no solution other than all values being 0. There will be an infinitude of other solutions only when the system of equations has enough dependencies (linearly dependent equations) that the number of independent equations is at most N − 1.

  8. Abel–Ruffini theorem - Wikipedia

    en.wikipedia.org/wiki/Abel–Ruffini_theorem

    The fact that every polynomial equation of positive degree has solutions, possibly non-real, was asserted during the 17th century, but completely proved only at the beginning of the 19th century. This is the fundamental theorem of algebra , which does not provide any tool for computing exactly the solutions, although Newton's method allows ...

  9. Equation - Wikipedia

    en.wikipedia.org/wiki/Equation

    The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables.