write the relation between A.m and G.M
Answers
Hyy!!☺️
Derivation of AM × HM = GM2
Arithmetic Progression
x,AM,y → arithmetic progression
Taking the common difference of arithmetic progression,
AM−x=y−AM
x+y=2AM → Equation (1)
Geometric Progression
x,GM,y → geometric progression
The common ratio of this geometric progression is
GMx=yGM
xy=GM2 → Equation (2)
Harmonic Progression
x,HM,y → harmonic progression
1x,1HM,1y → the reciprocal of each term will form an arithmetic progression
The common difference is
1HM−1x=1y−1HM
2HM=1y+1x
2HM=x+yxy → Equation (3)
Substitute x + y = 2AM from Equation (1) and xy = GM2 from Equation (2) to Equation (3)
2HM=2AMGM2
GM2=AM×HM → Okay!
Mark as brainliest☺️
Follow me up❤️
Answer:
A.M. >= G.M.
A.M.= a +b /2
G.M.=√ a.b
A.M. =G.M. when , a=b
Step-by-step explanation:
Ex. a=13 b=1
A.M.= a+b/2
= 13+1/2
= 7
G.M. = √a.b
= √ 13.1
√ 13
......= 7>√13
A.M.>G.M.