Asked by Abdela said yimer
For any pair of non negative integers a and b, show that the arthmetic mean between a and b is greater than or equal to the geometric mean bdtween them.
Answers
Answered by
bobpursley
arithemtic mean= a/2 + b/2
geometric mean: sqrt ab
show a/2 + b/2 > sqrtab
a+b>2sqrtab
a-2sqrt ab + b>0
(sqrta-sqrtb)^2>0
abs(sqrta-sqrtb)>0
and the abolute value of the difference is always +.
geometric mean: sqrt ab
show a/2 + b/2 > sqrtab
a+b>2sqrtab
a-2sqrt ab + b>0
(sqrta-sqrtb)^2>0
abs(sqrta-sqrtb)>0
and the abolute value of the difference is always +.
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