CA Foundation Exam > CA Foundation Questions > If x to the power 1/p=y to the power 1/q=z to...
Start Learning for Free
If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r?
Most Upvoted Answer
If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 ...
Solution:
Given:
x^(1/p) = y^(1/q) = z^(1/r)
xyz = 1
Let us assume:
k = x^(1/p) = y^(1/q) = z^(1/r)
Then k^p = x, k^q = y, and k^r = z
Substituting these values in the equation xyz=1, we get:
k^(p+q+r) = 1
Taking the logarithm of both sides, we get:
(p+q+r) log(k) = 0
Since k is positive, log(k) is also positive. Therefore, (p+q+r) must be equal to zero.
Hence, p+q+r=0.
We also know that k = x^(1/p) = y^(1/q) = z^(1/r). Therefore, we can write:
k^(p+q+r) = x^(q+r) y^(p+r) z^(p+q) = 1
Substituting p+q+r=0, we get:
x^(q+r) y^(p+r) z^(p+q) = x^(-p) y^(-q) z^(-r)
Multiplying both sides by x^p y^q z^r, we get:
x^q y^r z^p = 1
This implies that x, y, and z are the roots of the equation:
t^3 = 1
Therefore, x = y = z = 1.
Substituting this in p+q+r=0, we get:
p+q+r=0
Since x=y=z=1, we have:
k = x^(1/p) = y^(1/q) = z^(1/r) = 1
Therefore, p=q=r=0.
Hence, the values of p,q, and r are 0.
Given:
x^(1/p) = y^(1/q) = z^(1/r)
xyz = 1
Let us assume:
k = x^(1/p) = y^(1/q) = z^(1/r)
Then k^p = x, k^q = y, and k^r = z
Substituting these values in the equation xyz=1, we get:
k^(p+q+r) = 1
Taking the logarithm of both sides, we get:
(p+q+r) log(k) = 0
Since k is positive, log(k) is also positive. Therefore, (p+q+r) must be equal to zero.
Hence, p+q+r=0.
We also know that k = x^(1/p) = y^(1/q) = z^(1/r). Therefore, we can write:
k^(p+q+r) = x^(q+r) y^(p+r) z^(p+q) = 1
Substituting p+q+r=0, we get:
x^(q+r) y^(p+r) z^(p+q) = x^(-p) y^(-q) z^(-r)
Multiplying both sides by x^p y^q z^r, we get:
x^q y^r z^p = 1
This implies that x, y, and z are the roots of the equation:
t^3 = 1
Therefore, x = y = z = 1.
Substituting this in p+q+r=0, we get:
p+q+r=0
Since x=y=z=1, we have:
k = x^(1/p) = y^(1/q) = z^(1/r) = 1
Therefore, p=q=r=0.
Hence, the values of p,q, and r are 0.
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
If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r?
Question Description
If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r? 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 If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r?.
If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r? 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 If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r?.
Solutions for If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r? 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 If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r? defined & explained in the simplest way possible. Besides giving the explanation of
If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r?, a detailed solution for If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r? has been provided alongside types of If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r? theory, EduRev gives you an
ample number of questions to practice If x to the power 1/p=y to the power 1/q=z to the power 1/r and xyx=1 then find value of p q r? 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