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
- With the rise of both parts of the equation are irrational to one extent
- Using the change of variables
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:
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: