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If b c/a= c a/b=a b/c and a b c is not equal to zero then show that each of these ratios is equal to 2 also prove that A2 b2 c2= ab BC Ba?
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If b c/a= c a/b=a b/c and a b c is not equal to zero then show that ea...
Solution:
Proving b c/a = c a/b = a b/c = 2:
Let b c/a = k. Then, c/a = 1/k and b/a = k. Multiplying these three ratios, we get:
b c/a * c a/b * a b/c = k * 1/k * k = k^2 = 1
Therefore, k = ±1. But a, b, and c are not equal to zero. So, k cannot be equal to -1. Hence, k = 1.
Therefore, b c/a = c a/b = a b/c = 2.
Proving A2 b2 c2 = ab BC Ca:
We know that b c/a = 2. So, c = 2 a/b.
Substituting this value of c in the equation a b c = A, we get:
a b (2 a/b) = A
2 a^2 = A
Squaring both sides, we get:
4 a^4 = A^2
Similarly, we can find the values of B^2 and C^2 as:
4 b^4 = B^2
4 c^4 = C^2
Multiplying these three equations, we get:
64 a^4 b^4 c^4 = A^2 B^2 C^2
But we know that a b c = A.
Therefore, A^2 = a^2 B^2 = b^2 C^2 = c^2 A^2.
Multiplying these four equations, we get:
A^2 B^2 C^2 a^2 b^2 c^2 = a^2 b^2 c^2 A^2 B^2 C^2
A^2 B^2 C^2 = a^2 b^2 c^2
Therefore, A^2 b^2 c^2 = a^2 B^2 c^2 = a^2 b^2 C^2 = ab BC Ca.
Hence, proved.
Proving b c/a = c a/b = a b/c = 2:
Let b c/a = k. Then, c/a = 1/k and b/a = k. Multiplying these three ratios, we get:
b c/a * c a/b * a b/c = k * 1/k * k = k^2 = 1
Therefore, k = ±1. But a, b, and c are not equal to zero. So, k cannot be equal to -1. Hence, k = 1.
Therefore, b c/a = c a/b = a b/c = 2.
Proving A2 b2 c2 = ab BC Ca:
We know that b c/a = 2. So, c = 2 a/b.
Substituting this value of c in the equation a b c = A, we get:
a b (2 a/b) = A
2 a^2 = A
Squaring both sides, we get:
4 a^4 = A^2
Similarly, we can find the values of B^2 and C^2 as:
4 b^4 = B^2
4 c^4 = C^2
Multiplying these three equations, we get:
64 a^4 b^4 c^4 = A^2 B^2 C^2
But we know that a b c = A.
Therefore, A^2 = a^2 B^2 = b^2 C^2 = c^2 A^2.
Multiplying these four equations, we get:
A^2 B^2 C^2 a^2 b^2 c^2 = a^2 b^2 c^2 A^2 B^2 C^2
A^2 B^2 C^2 = a^2 b^2 c^2
Therefore, A^2 b^2 c^2 = a^2 B^2 c^2 = a^2 b^2 C^2 = ab BC Ca.
Hence, proved.
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If b c/a= c a/b=a b/c and a b c is not equal to zero then show that each of these ratios is equal to 2 also prove that A2 b2 c2= ab BC Ba?
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If b c/a= c a/b=a b/c and a b c is not equal to zero then show that each of these ratios is equal to 2 also prove that A2 b2 c2= ab BC Ba? 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 b c/a= c a/b=a b/c and a b c is not equal to zero then show that each of these ratios is equal to 2 also prove that A2 b2 c2= ab BC Ba? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If b c/a= c a/b=a b/c and a b c is not equal to zero then show that each of these ratios is equal to 2 also prove that A2 b2 c2= ab BC Ba?.
If b c/a= c a/b=a b/c and a b c is not equal to zero then show that each of these ratios is equal to 2 also prove that A2 b2 c2= ab BC Ba? 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 b c/a= c a/b=a b/c and a b c is not equal to zero then show that each of these ratios is equal to 2 also prove that A2 b2 c2= ab BC Ba? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If b c/a= c a/b=a b/c and a b c is not equal to zero then show that each of these ratios is equal to 2 also prove that A2 b2 c2= ab BC Ba?.
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