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If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in HP.?
Verified Answer
If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in H...
Given that A, B, C are in AP and C, B, A are in GP
A = (C + B) / 2
and C = AB/B
Substituting the value of C in A we get
A = (AB/B + B) / 2
A = (AB + B^2) / (2B)
Therefore, A, C, B are in HP.
A = (C + B) / 2
and C = AB/B
Substituting the value of C in A we get
A = (AB/B + B) / 2
A = (AB + B^2) / (2B)
Therefore, A, C, B are in HP.
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If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in H...
Proof that A, C, B are in HP
Given information:- B, A, C are in AP: B, A, C are in arithmetic progression, so 2A = B + C.
- C, B, A are in GP: C, B, A are in geometric progression, so B^2 = AC.
Proof:- Since B, A, C are in AP, we have 2A = B + C.
- Rearranging this equation, we get C = 2A - B.
- Since C, B, A are in GP, we have B^2 = AC.
- Substituting the value of C from the first equation into the second equation, we get B^2 = A(2A - B).
- Simplifying this equation, we get B^2 = 2A^2 - AB.
- Rearranging this equation, we get AB = 2A^2 - B^2.
- Dividing by AB on both sides, we get 1 = 2A/B - B/A.
- This equation represents the harmonic mean of A and B with respect to C.
- Therefore, A, C, B are in HP (Harmonic Progression).
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If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in HP.?
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If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in HP.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in HP.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in HP.?.
If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in HP.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in HP.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If B,A,C are in ap and C,B,A are in gp then proved that A,C,B are in HP.?.
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