RD Sharma Class 9 Solutions Chapter 4 Exercise 4.3: Clear your exams with the RD Sharma Solutions Class 9 Maths. You can easily download the PDF of RD Sharma Class 9 Solutions Chapter 4 Exercise 4.3. All the solutions are as per the current CBSE syllabus and are easy to understand. To know more, read the whole blog.
Download RD Sharma Class 9 Solutions Chapter 4 Exercise 4.3 PDF
RD Sharma Class 9 Solutions Chapter 4 Exercise 4.3
Access RD Sharma Class 9 Solutions Chapter 4 Exercise 4.3
Question 1: Find the cube of each of the following binomial expressions:
(i) (1/x + y/3)
(ii) (3/x – 2/x2)
(iii) (2x + 3/x)
(iv) (4 – 1/3x)
Solution:
[Using identities: (a + b)3 = a3 + b3 + 3ab(a + b) and (a – b)3 = a3 – b3 – 3ab(a – b) ]
(i)
(ii)
(iii)
(iv)
Question 2: Simplify each of the following:
(i) (x + 3)3 + (x – 3) 3
(ii) (x/2 + y/3) 3 – (x/2 – y/3) 3
(iii) (x + 2/x) 3 + (x – 2/x) 3
(iv) (2x – 5y) 3 – (2x + 5y) 3
Solution:
[Using identities:
a3 + b3 = (a + b)(a2 + b2 – ab)
a3 – b3 = (a – b)(a2 + b2 + ab)
(a + b)(a-b) = a2 – b2
(a + b)2 = a2 + b2 + 2ab and
(a – b)2 = a2 + b2 – 2ab]
(i) (x + 3)3 + (x – 3) 3
Here a = (x + 3), b = (x – 3)
(ii) (x/2 + y/3) 3 – (x/2 – y/3) 3
Here a = (x/2 + y/3) and b = (x/2 – y/3)
(iii) (x + 2/x) 3 + (x – 2/x) 3
Here a = (x + 2/x) and b = (x – 2/x)
(iv) (2x – 5y) 3 – (2x + 5y) 3
Here a = (2x – 5y) and b = 2x + 5y
Question 3: If a + b = 10 and ab = 21, find the value of a3 + b3.
Solution:
a + b = 10, ab = 21 (given)
Choose a + b = 10
Cubing both sides,
(a + b)3 = (10)3
a3 + b3 + 3ab(a + b) = 1000
a3 + b3 + 3 x 21 x 10 = 1000 (using given values)
a3 + b3 + 630 = 1000
a3 + b3 = 1000 – 630 = 370
or a3 + b3 = 370
Question 4: If a – b = 4 and ab = 21, find the value of a3 – b3.
Solution:
a – b = 4, ab= 21 (given)
Choose a – b = 4
Cubing both sides,
(a – b)3 = (4)3
a3 – b3 – 3ab (a – b) = 64
a3 – b3 – 3 × 21 x 4 = 64 (using given values)
a3 – b3 – 252 = 64
a3 – b3 = 64 + 252
= 316
Or a3 – b3 = 316
Question 5: If x + 1/x = 5, find the value of x3 + 1/x3 .
Solution:
Given: x + 1/x = 5
Apply Cube on x + 1/x
Question 6: If x – 1/x = 7, find the value of x3 – 1/x3 .
Solution:
Given: x – 1/x = 7
Apply Cube on x – 1/x
Question 7: If x – 1/x = 5, find the value of x3 – 1/x3 .
Solution:
Given: x – 1/x = 5
Apply Cube on x – 1/x
Question 8: If (x2 + 1/x2) = 51, find the value of x3 – 1/x3.
Solution:
We know that: (x – y)2 = x2 + y2 – 2xy
Replace y with 1/x, we get
(x – 1/x)2 = x2 + 1/x2 – 2
Since (x2 + 1/x2) = 51 (given)
(x – 1/x)2 = 51 – 2 = 49
or (x – 1/x) = ±7
Now, Find x3 – 1/x3
We know that, x3 – y3 = (x – y)(x2 + y2 + xy)
Replace y with 1/x, we get
x3 – 1/x3 = (x – 1/x)(x2 + 1/x2 + 1)
Use (x – 1/x) = 7 and (x2 + 1/x2) = 51
x3 – 1/x3 = 7 x 52 = 364
x3 – 1/x3 = 364
Question 9: If (x2 + 1/x2) = 98, find the value of x3 + 1/x3.
Solution:
We know that: (x + y)2 = x2 + y2 + 2xy
Replace y with 1/x, we get
(x + 1/x)2 = x2 + 1/x2 + 2
Since (x2 + 1/x2) = 98 (given)
(x + 1/x)2 = 98 + 2 = 100
or (x + 1/x) = ±10
Now, Find x3 + 1/x3
We know that, x3 + y3 = (x + y)(x2 + y2 – xy)
Replace y with 1/x, we get
x3 + 1/x3 = (x + 1/x)(x2 + 1/x2 – 1)
Use (x + 1/x) = 10 and (x2 + 1/x2) = 98
x3 + 1/x3 = 10 x 97 = 970
x3 + 1/x3 = 970
Question 10: If 2x + 3y = 13 and xy = 6, find the value of 8x3 + 27y3.
Solution:
Given: 2x + 3y = 13, xy = 6
Cubing 2x + 3y = 13 both sides, we get
(2x + 3y)3 = (13)3
(2x)3 + (3y) 3 + 3( 2x )(3y) (2x + 3y) = 2197
8x3 + 27y3 + 18xy(2x + 3y) = 2197
8x3 + 27y3 + 18 x 6 x 13 = 2197
8x3 + 27y3 + 1404 = 2197
8x3 + 27y3 = 2197 – 1404 = 793
8x3 + 27y3 = 793
Question 11: If 3x – 2y= 11 and xy = 12, find the value of 27x3 – 8y3.
Solution:
Given: 3x – 2y = 11 and xy = 12
Cubing 3x – 2y = 11 both sides, we get
(3x – 2y)3 = (11)3
(3x)3 – (2y)3 – 3 ( 3x)( 2y) (3x – 2y) =1331
27x3 – 8y3 – 18xy(3x -2y) =1331
27x3 – 8y3 – 18 x 12 x 11 = 1331
27x3 – 8y3 – 2376 = 1331
27x3 – 8y3 = 1331 + 2376 = 3707
27x3 – 8y3 = 3707
This is the complete blog of RD Sharma Solutions Class 9 Maths Chapter 4 Exercise 4.3. To know more about the CBSE Class 9 Maths, ask in the comments.
FAQs on RD Sharma Class 9 Solutions Chapter 4 Exercise 4.3
How much does it cost to download the PDF of RD Sharma Solutions for Class 9 Maths Chapter 4 Exercise 4.3?
You can download it for free.
How many questions are there in RD Sharma Solutions for Class 9 Maths Chapter 4 Exercise 4.3?
There are 19 questions in RD Sharma Solutions Class 9 Maths Chapter 4 Exercise 4.3.
From where can I download the PDF of RD Sharma Solutions Class 9 Maths Chapter 4 Exercise 4.3?
You can find the download link from the above blog.