1. Chapter 8 Class 11 Sequences and Series
  2. Serial order wise
  3. Ex 8.2
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Ex 8.2, 29 - Chapter 8 Class 11 Sequences and Series

Last updated at Dec. 16, 2024 by Teachoo

Transcript

Ex 8.2, 29 If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A ((A+G)(A G)) Let a & b be two numbers We need to show that the numbers are A ((A+G)(A G)) i.e. a = A + (( + )( )) b = A (( + )( )) Now we know that Arithmetic mean =A = ( a+b)/2 Geometric mean =G= ab Putting value of A and G in RHS we can prove it is equal to a and b Solving A (( + )( )) = A ( 2 2) Putting A = ( + )/2 & G = = (( + )/2) ((( + )/2)^2 ( )2) = (( + )/2) ((( + )2 )/4 ) = (( + )/2) (( 2+ 2+2 4 )/4) = (( + )/2) (( 2 + 2 2 )/4) = ( + )/2 (( )2/4) = ( + )/2 ((( )/2)^2 ) = ( + )/2 ( )/2 Thus, A + (( + )( )) = a & A (( + )( )) = b Hence proved.
  1. Chapter 8 Class 11 Sequences and Series
  2. Serial order wise

    3. Ex 8.2

    Examples →
Examples →
Chapter 8 Class 11 Sequences and Series
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo