Last updated at May 29, 2018 by Teachoo

Transcript

Ex 9.3, 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.

Ex 9.3

Ex 9.3, 1

Ex 9.3, 2

Ex 9.3, 3 Important

Ex 9.3, 4

Ex 9.3, 5

Ex 9.3, 6

Ex 9.3, 7

Ex 9.3, 8

Ex 9.3, 9

Ex 9.3, 10

Ex 9.3, 11 Important

Ex 9.3, 12

Ex 9.3, 13

Ex 9.3, 14

Ex 9.3, 15

Ex 9.3, 16

Ex 9.3, 17 Important

Ex 9.3, 18 Important

Ex 9.3, 19

Ex 9.3, 20

Ex 9.3, 21

Ex 9.3, 22 Important

Ex 9.3, 23

Ex 9.3, 24

Ex 9.3, 25

Ex 9.3, 26

Ex 9.3, 27 Important

Ex 9.3, 28 Important

Ex 9.3, 29 Important You are here

Ex 9.3, 30

Ex 9.3, 31

Ex 9.3, 32

Chapter 9 Class 11 Sequences and Series

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.