GMAT Exam > GMAT Questions > The positive value of x that satisfies the eq...
Start Learning for Free
The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is between
- a)0 and 0.5
- b)0.5 and 1
- c)1 and 1.5
- d)1.5 and 2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3...
Solution:
Given, (1-2x)^5 = (1-3x)^4
Let's expand the two expressions using binomial theorem,
(1-2x)^5 = 1 - 10x + 40x^2 - 80x^3 + 80x^4 - 32x^5
(1-3x)^4 = 1 - 12x + 54x^2 - 108x^3 + 81x^4
Now, equating the two expressions we get,
1 - 10x + 40x^2 - 80x^3 + 80x^4 - 32x^5 = 1 - 12x + 54x^2 - 108x^3 + 81x^4
Simplifying the above expression, we get
32x^5 - 161x^4 + 274x^3 - 166x^2 + 22x = 0
We can factor out x from the above expression,
x(32x^4 - 161x^3 + 274x^2 - 166x + 22) = 0
Since we are looking for a positive value of x, we can ignore the first factor x=0.
Now, we are left with the equation 32x^4 - 161x^3 + 274x^2 - 166x + 22 = 0
We can use Newton-Raphson method to find the positive root of the above equation.
After solving using Newton-Raphson method, we get the positive root of the equation to be approximately 1.2.
Therefore, the positive value of x that satisfies the given equation is between 1 and 1.5, which is option C.
Given, (1-2x)^5 = (1-3x)^4
Let's expand the two expressions using binomial theorem,
(1-2x)^5 = 1 - 10x + 40x^2 - 80x^3 + 80x^4 - 32x^5
(1-3x)^4 = 1 - 12x + 54x^2 - 108x^3 + 81x^4
Now, equating the two expressions we get,
1 - 10x + 40x^2 - 80x^3 + 80x^4 - 32x^5 = 1 - 12x + 54x^2 - 108x^3 + 81x^4
Simplifying the above expression, we get
32x^5 - 161x^4 + 274x^3 - 166x^2 + 22x = 0
We can factor out x from the above expression,
x(32x^4 - 161x^3 + 274x^2 - 166x + 22) = 0
Since we are looking for a positive value of x, we can ignore the first factor x=0.
Now, we are left with the equation 32x^4 - 161x^3 + 274x^2 - 166x + 22 = 0
We can use Newton-Raphson method to find the positive root of the above equation.
After solving using Newton-Raphson method, we get the positive root of the equation to be approximately 1.2.
Therefore, the positive value of x that satisfies the given equation is between 1 and 1.5, which is option C.
Free Test
FREE
| Start Free Test |
Community Answer
The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3...
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer?
Question Description
The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer?.
The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer?.
Solutions for The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The positive value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is betweena)0 and 0.5b)0.5 and 1c)1 and 1.5d)1.5 and 2Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
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