Irrational equations

The concept of the irrational equation

Definition: an Irrational equation is an equation containing the variable under the root sign of the first degree.

Solution of irrational equations

  1. With the rise of both parts of the equation are irrational to one extent
  2. In the presentation of both parts of the equation to the degree is odd (1,3,5,7....) the resulting equation is equivalent to a given ( DHS)

    Example 1:

    Rozwarte equation:

    Solutions:

    Answer:

    In the presentation of both sides of the pair degree in (2,4,6,8....) can appear extraneous roots, which will eliminate checking.

    Example 2:

    Rozwarte equation:

    Solutions:

    Check: When you have is not a correct equation, therefore, is an extraneous root.

    If you have - a true equality, therefore, is the root of the given equation.

    Answer:

  3. Using the change of variables
  4. If in the equation variable occurs in the same form, suchno the corresponding expression with a variable to mark one letter (a new variable).

    Example 3:

    Rozwarte equation:

    Solution: Let Us Denote Then

    We obtain the equation:

    Reverse the substitution: Then or here .

    If you have - a true equality, therefore, is the root of the given equation.

    Answer:

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