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For a,b,c > 0 the value of each ratio is a/b c= b/c a= c/a b then find the value of each ratio if a b c ≠ 0?
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For a,b,c > 0 the value of each ratio is a/b c= b/c a= c/a b then find...
Solution:
Given, a/b = b/c = c/a = k (say)
We need to find the value of k.
Let’s consider the first ratio a/b = k.
We can write this as a = kb.
Similarly, b/c = k can be written as b = kc.
Finally, c/a = k can be written as c = ka.
Now, we can substitute the values of a, b and c in terms of k in the given ratios.
a/b = k can be written as kb/b = k
Similarly, b/c = k can be written as kc/c = k
And, c/a = k can be written as ka/a = k
Now, we can simplify these ratios.
kb/b = k can be simplified as k^2 = 1/k
kc/c = k can be simplified as k^2 = 1/k
ka/a = k can be simplified as k^2 = 1/k
From the above three equations, we get k^3 = 1.
Therefore, k = 1 or k = -1/2 ± i√3/2 (where i is the imaginary unit)
However, since a, b, c are positive, k cannot be negative or imaginary.
Therefore, k = 1.
Hence, a/b = b/c = c/a = 1.
Conclusion:
The value of each ratio is 1 if a, b, c ≠ 0.
Given, a/b = b/c = c/a = k (say)
We need to find the value of k.
Let’s consider the first ratio a/b = k.
We can write this as a = kb.
Similarly, b/c = k can be written as b = kc.
Finally, c/a = k can be written as c = ka.
Now, we can substitute the values of a, b and c in terms of k in the given ratios.
a/b = k can be written as kb/b = k
Similarly, b/c = k can be written as kc/c = k
And, c/a = k can be written as ka/a = k
Now, we can simplify these ratios.
kb/b = k can be simplified as k^2 = 1/k
kc/c = k can be simplified as k^2 = 1/k
ka/a = k can be simplified as k^2 = 1/k
From the above three equations, we get k^3 = 1.
Therefore, k = 1 or k = -1/2 ± i√3/2 (where i is the imaginary unit)
However, since a, b, c are positive, k cannot be negative or imaginary.
Therefore, k = 1.
Hence, a/b = b/c = c/a = 1.
Conclusion:
The value of each ratio is 1 if a, b, c ≠ 0.
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For a,b,c > 0 the value of each ratio is a/b c= b/c a= c/a b then find the value of each ratio if a b c ≠ 0?
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For a,b,c > 0 the value of each ratio is a/b c= b/c a= c/a b then find the value of each ratio if a b c ≠ 0? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about For a,b,c > 0 the value of each ratio is a/b c= b/c a= c/a b then find the value of each ratio if a b c ≠ 0? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a,b,c > 0 the value of each ratio is a/b c= b/c a= c/a b then find the value of each ratio if a b c ≠ 0?.
For a,b,c > 0 the value of each ratio is a/b c= b/c a= c/a b then find the value of each ratio if a b c ≠ 0? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about For a,b,c > 0 the value of each ratio is a/b c= b/c a= c/a b then find the value of each ratio if a b c ≠ 0? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a,b,c > 0 the value of each ratio is a/b c= b/c a= c/a b then find the value of each ratio if a b c ≠ 0?.
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