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X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is?
Most Upvoted Answer
X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is?
Explanation:
Solution:
Given, X^1/p=y^1/q=z^1/r and xyz=1
We need to find the value of p, q, and r.
Solution:
Step 1: Express X, Y, and Z in terms of p, q, and r
As per the given equation,
X^1/p=y^1/q=z^1/r
Let's take the cube of all the terms,
X^3/p=y^3/q=z^3/r
Now, let's express X, Y, and Z in terms of p, q, and r
X = (X^3/p)^(1/3) = (Y^3/q)^(1/3) = (Z^3/r)^(1/3)
Y = (X^3/p)^(1/3) = (Y^3/q)^(1/3) = (Z^3/r)^(1/3)
Z = (X^3/p)^(1/3) = (Y^3/q)^(1/3) = (Z^3/r)^(1/3)
Step 2: Substitute the value of X, Y, and Z in xyz=1
xyz=1
(X*Y*Z) = 1
[(X^3/p)^(1/3)] * [(Y^3/q)^(1/3)] * [(Z^3/r)^(1/3)] = 1
[X^(3/p) * Y^(3/q) * Z^(3/r)]^(1/3) = 1
[X^(q*r) * Y^(p*r) * Z^(p*q)]^(1/3) = 1
X^(q*r) * Y^(p*r) * Z^(p*q) = 1
Step 3: Substitute the value of X, Y, and Z in X^3/p=y^3/q=z^3/r
X^3/p=y^3/q=z^3/r
Substituting the value of X, Y, and Z,
(X^(q*r))^3/p = (Y^(p*r))^3/q = (Z^(p*q))^3/r
X^(3q*r/p) = Y^(3p*r/q) = Z^(3p*q/r)
Step 4: Equate the exponents in the above two equations
X^(3q*r/p) = Y^(3p*r/q) = Z^(3p*q/r)
3q*r/p = 3p*r/q = 3p*q/r
q = 3p, r = 3q = 9p
Step 5: Find the value of p
q = 3p, r = 9p
Community Answer
X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is?
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X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is?
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X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is? 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 X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is?.
X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is? 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 X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X^1/p=y^1/q=z^1/r and xyz=1 ,then the value of p q r is?.
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