A10 simplest irrational equations option 1. Irrational equations

Irrational equations

Option 1
X
9
5

 x
2 2
x=3.
equation roots
1)(∞;1]; 2)(1;5]; 3)(5;10]; 4); 2)[1;2); 3)(2;2];4); 3)[2;3]; 4)(2;3].
3. Specify the interval to which they belong
zeros of the function f(x)=
1)[1;0]; 2)[1;1); 3)[3;1]; 4)[3;1).
4.Find the arithmetic mean of the roots
equations
x45
=0.
x.
2
- x
2

X

1)1; 2)
; 3)2; 4)
6 .
2
5. Find the largest root of the equation
1)=0.
2)(
x3
3
; 2)
; 3)3; 4)
3
2
.
22 
X
3
2
10 
10
3
xx41
7. Solve the equation
2 = x1. Find 3∙x0+2.
2 x
5
=|x+3|2.
1)
2 x
7
2
6. Solve the equation
7. Solve the equation
x 4
4 x
Option 3
6=0.
X
17
3=|x+2|.
1. Specify the interval to which they belong
roots of equation 1+
1)[1;2]; 2).
2. Specify the interval to which they belong
zeros of the function f(x)=
2 3x.
3 2 x
\u003d 2x.
x5
2
;
1
2
1)[0.7;0.7]; 2)(0;1]; 3)[1;0); 4)[
1
2
equation roots
+4=x.
1)(2;3); 2)(8;7); 3)(0;2); 4)(3;9).
4. How many roots does the equation have
= 1x².
2 2
 x
14
21
11

2
4
X
X
x


1) none; 2) one; 3) two; 4) four.
5.Solve the equation x+7=
. Specify
15 x
correct statement about its roots.
55
two roots, and they are of different signs
there are two roots, and they are positive
there is only one root, and it
there is only one root, and it
1)
2)
3)
positive
4)
negative
6. Find the largest root of the equation
Option 4
1. Specify the interval to which they belong
roots of the equation x+
1)(5;1); 2)(3;1]; 3)(2;1]; 4)(1;6).
2. Specify the interval to which they belong
zeros of the function f(x)=
2 2x.
5 
x1
=1.
1
X

1) [
1
2
;
1
2
]; 2) [0.6;0.6]; 3).
X

).
 x
52
1
2
3. Specify the interval to which they belong
equation roots
one); 2)(1;3); 3); 4)(2;0).
4. Specify the interval to which they belong
equation roots
1)(2;0); 2)(0;2); 3)(2;4); 4)(3;6).
5. Find the smallest root of the equation
=62x.
=x+2.
1)(4
)=0.
92 
3 x
7
5
5
X
X
2 x
7
3
1)
; 2)2; 3)8; 4)
6. Find the sum of the roots of the equation
23
3
.

X
7. Solve the equation 5=2|x|
 64
x -
2=x+4.

223
x
.
Option 6
Option 5

7
3 x
=x+3.
1. Specify the interval to which they belong
equation roots
1)(7;1.5); 2)(2,1;1];3); 4)(2;8).
2. Specify the interval to which they belong
zeros of the function f(x)=
1)[1;0]; 2)(2;1]; 3)(2;0]; 4)(1;+∞).
3. Let x0 be the smallest root of the equation:
x23
x.
2

 68
x -
2=x+6. Find 2x0.
x
1)0; 2)9; 3)4; 4) the equation has no roots.
4. Find the arithmetic mean of the roots
equations
x21 -
32
 x
=0.


7
X
1)1; 2)
5
2
; 3) no roots; 4) 5 .
5. Specify the interval to which they belong
equation roots
1)[6;5]; 2)[4;0]; 3); 4).
6. Let x0 be the smallest root of the equation:
=x5.
x5
 46
x -
x
7. Solve the equation
2=x+4. Find 2∙x01.
|4
|49
xx


4x=3.
1. Specify the interval to which they belong
zeros of the function f(x)=
1)[0.4;0.4]; 2)(0.6;0.6); 3) (0.7; 0.7); 4)[
1;0,6].
2.Find the sum of the roots of the equation
2 3x.
x4
 64
x -
2=x+4.
X
1)1; 2)7; 3)6; 4) the equation has no roots.
3. Find the arithmetic mean of the roots
equations
x57
2


1) 7; 2)1; 3)
; 4) no roots.
4. Specify the interval to which they belong
equation roots
1)(6;4); 2)(0;2); 3)(2;5); 4)(4;0).
5. Find the smallest root of the equation
(2
2)=0.
+x=3.
2 2
4 x
3 x
1
4
3
7
X
X


x2 = 0.
1
5
1)
8
3
; 2)
1
4
; 3)2; 4)
5
4
.
6. Let x0 be a non-positive root of the equation:
 24
x -
2 = x2. Find 2∙x0+1.
x
7. Solve the equation
4 x
13
=|x+1|3.
job number
Option 1
Answers "Irrational Equations"
Option 4
Option 2
Option 3
Option 5
Option 6
1
2
3
4
5
6
7
1
1
2
3
1
Ø
2
4
2
3
3
3
16
2
3
2
4
1
1
1
1;15
2
2
4
3
4
1
±19
2
2
3
2
4
3
0
3
1
2
4
1
Ø
9

Your privacy is important to us. For this reason, we have developed a Privacy Policy that describes how we use and store your information. Please read our privacy policy and let us know if you have any questions.

Collection and use of personal information

Personal information refers to data that can be used to identify a specific person or contact him.

You may be asked to provide your personal information at any time when you contact us.

The following are some examples of the types of personal information we may collect and how we may use such information.

What personal information we collect:

When you submit an application on the site, we may collect various information, including your name, phone number, email address, etc.

How we use your personal information:

The personal information we collect allows us to contact you and inform you about unique offers, promotions and other events and upcoming events.
From time to time, we may use your personal information to send you important notices and messages.
We may also use personal information for internal purposes, such as conducting audits, data analysis and various research in order to improve the services we provide and provide you with recommendations regarding our services.
If you enter a prize draw, contest or similar incentive, we may use the information you provide to administer such programs.

Disclosure to third parties

We do not disclose information received from you to third parties.

Exceptions:

In the event that it is necessary - in accordance with the law, judicial order, in legal proceedings, and / or based on public requests or requests from state bodies in the territory of the Russian Federation - disclose your personal information. We may also disclose information about you if we determine that such disclosure is necessary or appropriate for security, law enforcement, or other public interest purposes.
In the event of a reorganization, merger or sale, we may transfer the personal information we collect to the relevant third party successor.

Protection of personal information

We take precautions - including administrative, technical and physical - to protect your personal information from loss, theft, and misuse, as well as from unauthorized access, disclosure, alteration and destruction.

Maintaining your privacy at the company level

To ensure that your personal information is secure, we communicate privacy and security practices to our employees and strictly enforce privacy practices.

Irrational equations are equations in which the variable is contained under the sign of the root.

An irrational equation, as a rule, is reduced to an equivalent system containing equations and inequalities.

Of the two systems, choose the one that is easier to solve.

If , the equation is equivalent to the equation .

Irrational equations can also be solved by raising both sides of the equation to a natural power. When raising an equation to a power, extraneous roots may appear. Therefore, a necessary part of solving an irrational equation is a check.

Tasks and tests on the topic "Irrational Equations"

Irrational equations - Quadratic equations Grade 8
Lessons: 1 Assignments: 9 Tests: 1
Irrational equations and inequalities - Important topics for repeating the exam in mathematics
Jobs: 11
§4 Application of properties of functions to the solution of irrational equations
Lessons: 1 Assignments: 13
§2 Irrational equations - Section 4. Power function Grade 10
Lessons: 1 Assignments: 9
Systems of equations - Equations and inequalities Grade 11
Lessons: 1 Assignments: 19 Tests: 1

When solving irrational equations, as a rule, the following methods are used:
1) transition to an equivalent system (in this case, verification is not needed);
2) the method of raising both parts of the equation to the same degree;
3) the method of introducing new variables.

If you do not follow the equivalence of transitions, then checking is a mandatory element of the solution. O.D.Z. in irrational equations will not help you weed out all extraneous roots. Pay attention to this!

When solving irrational equations, as a rule, the following methods are used: 1) transition to an equivalent system (in this case, verification is not needed); 2) the method of raising both parts of the equation to the same degree; 3) the method of introducing new variables.

Examples.


x=-1

Solution: ODZ:

Let's square both sides of the equation:

x \u003d 6 is included in the ODZ, which means it can be the root of this equation.

Examination:

Solution: ODZ

y 2 + 4y - 12 = 0;

y 1 = -6, y 2 = 2.

a) = -6. There are no solutions, because -6>0, but 0.

b) = 2,
x - 3 = 4,
x = 7 is included in the ODZ.