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If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then - (i) a,b,c are in G.P. (ii) a,b/2,c are in A.P. (iii) a,b/2,c are in H.P. (iv) a,2b,c are in H.P.?
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If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then...
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If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then...
Solution:
Given, (1/a) (1/a-2b) (1/c) (1/c-2b) = 0
We need to find the relation between a, b, and c.
Case 1: If any one of the terms is zero, then the given equation is satisfied. But we need to remember that a, b, and c are not in A.P.
Case 2: Let none of the terms is zero. Therefore, the product of the four terms is zero only when one or more of the terms are infinite.
So, either a = 0 or 2b = a or c = 0 or 2b = c.
We know that a, b, and c are not in A.P. Therefore, a cannot be equal to 2b or c. Hence, a = 0 or c = 0.
Case 2.1: If a = 0, then the given expression becomes zero, irrespective of the values of b and c.
Case 2.2: If c = 0, then the given expression becomes zero, irrespective of the values of a and b.
Therefore, we can conclude that a and c cannot be zero at the same time.
Hence, a and c are non-zero.
Therefore, the only possibility left is that 2b = a = c.
Therefore, a, b, and c are in G.P.
Answer: (i) a, b, and c are in G.P.
Given, (1/a) (1/a-2b) (1/c) (1/c-2b) = 0
We need to find the relation between a, b, and c.
Case 1: If any one of the terms is zero, then the given equation is satisfied. But we need to remember that a, b, and c are not in A.P.
Case 2: Let none of the terms is zero. Therefore, the product of the four terms is zero only when one or more of the terms are infinite.
So, either a = 0 or 2b = a or c = 0 or 2b = c.
We know that a, b, and c are not in A.P. Therefore, a cannot be equal to 2b or c. Hence, a = 0 or c = 0.
Case 2.1: If a = 0, then the given expression becomes zero, irrespective of the values of b and c.
Case 2.2: If c = 0, then the given expression becomes zero, irrespective of the values of a and b.
Therefore, we can conclude that a and c cannot be zero at the same time.
Hence, a and c are non-zero.
Therefore, the only possibility left is that 2b = a = c.
Therefore, a, b, and c are in G.P.
Answer: (i) a, b, and c are in G.P.
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If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then...
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If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then - (i) a,b,c are in G.P. (ii) a,b/2,c are in A.P. (iii) a,b/2,c are in H.P. (iv) a,2b,c are in H.P.?
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If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then - (i) a,b,c are in G.P. (ii) a,b/2,c are in A.P. (iii) a,b/2,c are in H.P. (iv) a,2b,c are in H.P.? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then - (i) a,b,c are in G.P. (ii) a,b/2,c are in A.P. (iii) a,b/2,c are in H.P. (iv) a,2b,c are in H.P.? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then - (i) a,b,c are in G.P. (ii) a,b/2,c are in A.P. (iii) a,b/2,c are in H.P. (iv) a,2b,c are in H.P.?.
If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then - (i) a,b,c are in G.P. (ii) a,b/2,c are in A.P. (iii) a,b/2,c are in H.P. (iv) a,2b,c are in H.P.? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then - (i) a,b,c are in G.P. (ii) a,b/2,c are in A.P. (iii) a,b/2,c are in H.P. (iv) a,2b,c are in H.P.? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then - (i) a,b,c are in G.P. (ii) a,b/2,c are in A.P. (iii) a,b/2,c are in H.P. (iv) a,2b,c are in H.P.?.
Solutions for If( 1/a) + (1/a-2b)+ (1/c) +(1/c-2b)=0 and a,b,c are not in A.P. ,then - (i) a,b,c are in G.P. (ii) a,b/2,c are in A.P. (iii) a,b/2,c are in H.P. (iv) a,2b,c are in H.P.? in English & in Hindi are available as part of our courses for JEE.
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