Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RD Sharma (Very Short Answer Questions): Algebraic Identities
Class 9 Maths Question Answers - Algebraic Identities
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Page 1
Q u e s t i o n : 5 2
If x +
1
x
= 3, then find the value of x
2
+
1
x
2
.
S o l u t i o n :
Page 2
Q u e s t i o n : 5 2
If x +
1
x
= 3, then find the value of x
2
+
1
x
2
.
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting the value of we get,
By transposing + 2 to left hand side, we get
Hence the value of is .
Q u e s t i o n : 5 3
If x +
1
x
= 3
, then find the value of x
6
+
1
x
6
.
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
Page 3
Q u e s t i o n : 5 2
If x +
1
x
= 3, then find the value of x
2
+
1
x
2
.
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting the value of we get,
By transposing + 2 to left hand side, we get
Hence the value of is .
Q u e s t i o n : 5 3
If x +
1
x
= 3
, then find the value of x
6
+
1
x
6
.
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting the value of We get,
By transposing + 2 to left hand side, we get
Cubing on both sides we get,
Using identity
(a +b)
3
= a
3
+b
3
+3ab(a +b)
Here
Put we get
By transposing 21 to left hand side we get ,
Hence the value of is .
Q u e s t i o n : 5 4
If a + b = 7 and ab = 12, find the value of a
2
+ b
2
S o l u t i o n :
We have to find the value of
Given
Using identity
By substituting the value of we get
By transposing +24 to left hand side we get ,
Page 4
Q u e s t i o n : 5 2
If x +
1
x
= 3, then find the value of x
2
+
1
x
2
.
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting the value of we get,
By transposing + 2 to left hand side, we get
Hence the value of is .
Q u e s t i o n : 5 3
If x +
1
x
= 3
, then find the value of x
6
+
1
x
6
.
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting the value of We get,
By transposing + 2 to left hand side, we get
Cubing on both sides we get,
Using identity
(a +b)
3
= a
3
+b
3
+3ab(a +b)
Here
Put we get
By transposing 21 to left hand side we get ,
Hence the value of is .
Q u e s t i o n : 5 4
If a + b = 7 and ab = 12, find the value of a
2
+ b
2
S o l u t i o n :
We have to find the value of
Given
Using identity
By substituting the value of we get
By transposing +24 to left hand side we get ,
Hence the value of is .
Q u e s t i o n : 5 5
If a - b = 5 and ab = 12, find the value of a
2
+ b
2
.
S o l u t i o n :
We have to find the value
Given
Using identity
By substituting the value of we get ,
By transposing – 24 to left hand side we get
Hence the value of is .
Q u e s t i o n : 5 6
If x -
1
x
=
1
2
, then write the value of 4x
2
+
4
x
2
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting the value of we get
By transposing – 2 to left hand side we get
Page 5
Q u e s t i o n : 5 2
If x +
1
x
= 3, then find the value of x
2
+
1
x
2
.
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting the value of we get,
By transposing + 2 to left hand side, we get
Hence the value of is .
Q u e s t i o n : 5 3
If x +
1
x
= 3
, then find the value of x
6
+
1
x
6
.
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting the value of We get,
By transposing + 2 to left hand side, we get
Cubing on both sides we get,
Using identity
(a +b)
3
= a
3
+b
3
+3ab(a +b)
Here
Put we get
By transposing 21 to left hand side we get ,
Hence the value of is .
Q u e s t i o n : 5 4
If a + b = 7 and ab = 12, find the value of a
2
+ b
2
S o l u t i o n :
We have to find the value of
Given
Using identity
By substituting the value of we get
By transposing +24 to left hand side we get ,
Hence the value of is .
Q u e s t i o n : 5 5
If a - b = 5 and ab = 12, find the value of a
2
+ b
2
.
S o l u t i o n :
We have to find the value
Given
Using identity
By substituting the value of we get ,
By transposing – 24 to left hand side we get
Hence the value of is .
Q u e s t i o n : 5 6
If x -
1
x
=
1
2
, then write the value of 4x
2
+
4
x
2
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting the value of we get
By transposing – 2 to left hand side we get
By taking least common multiply we get
By multiplying 4 on both sides we get
Hence the value of is
Q u e s t i o n : 5 7
If a
2
+
1
a
2
= 102
, find the value of a -
1
a
.
S o l u t i o n :
We have to find the value of
Given
Using identity
Here
By substituting we get
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FAQs on Class 9 Maths Question Answers - Algebraic Identities
| 1. What are algebraic identities? |  |
Ans. Algebraic identities are mathematical expressions that remain true regardless of the values of the variables involved. They are used to simplify and solve algebraic equations.
| 2. What are some commonly used algebraic identities? | |
Ans. Some commonly used algebraic identities include:
- $(a+b)^2 = a^2 + 2ab + b^2$
- $(a-b)^2 = a^2 - 2ab + b^2$
- $a^2 - b^2 = (a+b)(a-b)$
- $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$
- $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$
| 3. How are algebraic identities useful in solving equations? | |
Ans. Algebraic identities allow us to simplify complex equations by replacing certain expressions with their equivalent forms using the identities. This makes solving equations easier and helps in finding solutions quickly.
| 4. Can algebraic identities be applied to any equation? | |
Ans. Algebraic identities can be applied to equations that involve algebraic expressions. However, it is important to ensure that the identities used are applicable to the specific equation being solved.
| 5. How can I practice using algebraic identities? | |
Ans. To practice using algebraic identities, you can solve various algebraic equations that involve variables and apply the identities to simplify them. You can also solve algebraic expression-based problems and substitute values to verify the validity of the identities. Additionally, practicing exercises and problems from textbooks or online resources specifically focusing on algebraic identities will help improve your understanding and application of these identities.
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