Asked by Bea
the arithmetic mean of two numbers exceeds their geometric mean by two. find the numbers if one is 40 less than other?
please help me to answer this homework.
please help me to answer this homework.
Answers
Answered by
Reiny
smaller number --- x
larger number ---- x+40
arithmetic mean = (x + x+40)/2 = x+20
geometric mean = √(x(x+40))
x+20 - 2 = √(x^2 + 40x)
square both sides
x^2 + 36x + 324 = x^2 + 40x
324 = 4x
x = 81
one number is 81 and the other is 121
check:
AM = (81+121)/2 = 101
GM = √(81x121) = 99
The AM exceed the GM by 2
My answer is correct
larger number ---- x+40
arithmetic mean = (x + x+40)/2 = x+20
geometric mean = √(x(x+40))
x+20 - 2 = √(x^2 + 40x)
square both sides
x^2 + 36x + 324 = x^2 + 40x
324 = 4x
x = 81
one number is 81 and the other is 121
check:
AM = (81+121)/2 = 101
GM = √(81x121) = 99
The AM exceed the GM by 2
My answer is correct
Answered by
Jerome
Where do you get x + 20?
Answered by
Kayla
121 :)
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