CBSE Class 10 Answered
If 1/a,1/b,1/c are in a.p show that a(b+c),b(c+a),c (a+b) are in a.p
Asked by | 27 Oct, 2012, 09:01: AM
Expert Answer
Answer : Given :If 1/a,1/b,1/c are in a.p
To prove : a(b+c),b(c+a),c (a+b) are also in a.p
1/a, 1/b, 1/c are in AP
=> (1/a) + (1/c) = 2(1/b) {x, y, z are in AP iff : x + z = 2y}
=> (c+a) / (ca) = 2/b
=> b(c+a) = 2(ca)
(bc+ab) = 2(ca) ................... (1)
1/a, 1/b, 1/c are in AP
=> (1/a) + (1/c) = 2(1/b) {x, y, z are in AP iff : x + z = 2y}
=> (c+a) / (ca) = 2/b
=> b(c+a) = 2(ca)
(bc+ab) = 2(ca) ................... (1)
now , a(b+c) + c(a+b)
= ab + ca + ca + bc
= (bc+ab) + 2(ca)
= (bc+ab) + (bc+ab) ............ from (1)
= 2(bc+ab)
=> a(b+c) + c(a+b) = 2 b(c+a) {x, y, z are in AP iff : x + z = 2y}
= ab + ca + ca + bc
= (bc+ab) + 2(ca)
= (bc+ab) + (bc+ab) ............ from (1)
= 2(bc+ab)
=> a(b+c) + c(a+b) = 2 b(c+a) {x, y, z are in AP iff : x + z = 2y}
a(b+c),b(c+a),c (a+b) are in a.p
Hence Proved
Answered by | 27 Oct, 2012, 07:38: PM
Application Videos
-
Arithmetic Progression - 1
This video explains the concept of Arithmetic Progression, Solving Linear E... -
Sum of an n Terms of an A.P.
This video explains the concept of how to find the nth term of a Arithmetic... -
nth term of an A.P.
This video explains the concept of nth term of an Arithmetic Progression. -
Arithmetic Progression - 2
This video explains the concept of how to find an Arithmetic Progression. -
Nth term of an AP - 1
This video explains a case study based question covering the concept of ...
Concept Videos
-
Introduction to Arithmetic Progression
This video explains the identification of series which is mathematically kn... -
nth Term of an A.P.
Problems related to the calculation of nth term in an Arithmetic progressi... -
Determine terms of an arithmetic progression
Determine the terms of an arithmetic progression when given the number of t... -
Word Problems of A.P.
This video explains the concept of the nth term and the sum of the first n ... -
Introduction to Arithmetic Progression
This video explains the identification of series, mathematically known as A...
CBSE 10 - Maths
Asked by purbashadebnath1980 | 09 Mar, 2024, 12:10: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by deepikaselvam2009 | 20 Feb, 2024, 08:57: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by keshavsinghalhapur | 16 Jan, 2024, 08:46: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by keshavsinghalhapur | 15 Jan, 2024, 10:56: AM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by durgauikey7000 | 08 Dec, 2023, 08:16: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by skandachiranjeevin | 06 Dec, 2023, 07:08: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by shaikhyakub9946 | 30 Nov, 2023, 11:50: AM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by prassanna.j | 13 Nov, 2023, 11:24: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by prassanna.j | 13 Nov, 2023, 11:23: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by latayadav23 | 17 Oct, 2023, 08:39: PM
ANSWERED BY EXPERT
