CA Foundation Exam > CA Foundation Questions > Using (a–b)3 = a3 –b3 –3ab(a–b) tick the corr...
Start Learning for Free
Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these?
Most Upvoted Answer
Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/...
Solution:
Given: x = p1/3 – p–1/3
We need to find the correct option out of (a), (b), (c), and (d) using (a–b)3 = a3 –b3 –3ab(a–b).
Expansion of (a–b)3
(a–b)3 = a3 –b3 –3ab(a–b)
On putting a = p1/3 and b = p–1/3, we get
(p1/3 – p–1/3)3 = (p1/3)3 – (p–1/3)3 – 3(p1/3)(p–1/3)(p1/3 – p–1/3)
Simplifying the above expression, we get
p + 3p1/3 p–1/3(x) = 2p1/3 + 2p–1/3
Finding the value of x3 – 3x
Multiplying the above equation by p1/3, we get
p4/3 + 3p(x) – p2/3(x) = 2p + 2p2/3
Multiplying the above equation by p–2/3, we get
p1/3 + 3(x) – (x)(p–1/3) = 2p–1/3 + 2
Adding (x)(p–1/3) to both sides, we get
p1/3 + 3(x) = (x)(p1/3 + p–1/3) + 2p–1/3 + 2
Substituting the value of x = p1/3 – p–1/3, we get
p1/3 + 3(p1/3 – p–1/3) = (p1/3 – p–1/3)(p1/3 + p–1/3) + 2p–1/3 + 2
Simplifying the above expression, we get
3p1/3 – 3p–1/3 = p + 2p–1/3 + 2
Multiplying both sides by p1/3, we get
3p – 3 = p4/3 + 2p2/3 + 2p1/3
On simplifying the above expression, we get
p4/3 – 3p1/3 – 2p–1/3 – 3 = 0
Multiplying both sides by p1/3, we get
p5/3 – 3p2/3 – 2p1/3 – 3p1/3 = 0
p5/3 – 5p2/3 – 3p1/3 = 0
Multiplying both sides by p1/3, we get
p2 + 5p – 3 = 0
Solving the above quadratic equation, we get
p = (–5 ± √37)/2
Comparing the given options
(a) x3 3x = p 1/p
On substituting the value of x in the above
Given: x = p1/3 – p–1/3
We need to find the correct option out of (a), (b), (c), and (d) using (a–b)3 = a3 –b3 –3ab(a–b).
Expansion of (a–b)3
(a–b)3 = a3 –b3 –3ab(a–b)
On putting a = p1/3 and b = p–1/3, we get
(p1/3 – p–1/3)3 = (p1/3)3 – (p–1/3)3 – 3(p1/3)(p–1/3)(p1/3 – p–1/3)
Simplifying the above expression, we get
p + 3p1/3 p–1/3(x) = 2p1/3 + 2p–1/3
Finding the value of x3 – 3x
Multiplying the above equation by p1/3, we get
p4/3 + 3p(x) – p2/3(x) = 2p + 2p2/3
Multiplying the above equation by p–2/3, we get
p1/3 + 3(x) – (x)(p–1/3) = 2p–1/3 + 2
Adding (x)(p–1/3) to both sides, we get
p1/3 + 3(x) = (x)(p1/3 + p–1/3) + 2p–1/3 + 2
Substituting the value of x = p1/3 – p–1/3, we get
p1/3 + 3(p1/3 – p–1/3) = (p1/3 – p–1/3)(p1/3 + p–1/3) + 2p–1/3 + 2
Simplifying the above expression, we get
3p1/3 – 3p–1/3 = p + 2p–1/3 + 2
Multiplying both sides by p1/3, we get
3p – 3 = p4/3 + 2p2/3 + 2p1/3
On simplifying the above expression, we get
p4/3 – 3p1/3 – 2p–1/3 – 3 = 0
Multiplying both sides by p1/3, we get
p5/3 – 3p2/3 – 2p1/3 – 3p1/3 = 0
p5/3 – 5p2/3 – 3p1/3 = 0
Multiplying both sides by p1/3, we get
p2 + 5p – 3 = 0
Solving the above quadratic equation, we get
p = (–5 ± √37)/2
Comparing the given options
(a) x3 3x = p 1/p
On substituting the value of x in the above
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these?
Question Description
Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these?.
Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these?.
Solutions for Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these? defined & explained in the simplest way possible. Besides giving the explanation of
Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these?, a detailed solution for Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these? has been provided alongside types of Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these? theory, EduRev gives you an
ample number of questions to practice Using (a–b)3 = a3 –b3 –3ab(a–b) tick the correct of these when x = p1/3 – p–1/3 (a) x3 3x = p 1/p (b) x3 3x = p – 1/p (c) x3 3x = p 1 (d) none of these? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup