SOLUTION: The arithmetic mean of two numbers is 5 and the geometric means of the same numbers is 3.find the numbers
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Question 799680: The arithmetic mean of two numbers is 5 and the geometric means of the same numbers is 3.find the numbers
Found 2 solutions by josgarithmetic, thejackal:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
The two numbers are x and y.
and .
Substitute.
Square both sides.
x=9 or x=1
y=10-9 or y=10-1
y=1 or y=9
ANSWER: Either way, the two numbers are 9 and 1.
Answer by thejackal(72) (Show Source): You can put this solution on YOUR website!
Geometric mean: is the root of the products of the number
thus:
root(a.b) = 3
thus (a.b) = 3^2 = 9
Arithmetic mean: is the sum of the numbers divide by the number of number
thus:
(a+b)/2 = 5 or a+b = 10
b can be return as a function of a thus b = 10 - a
take this new function and use it in the first such that
(a.(10-a)) = 9
now you have a quadratic equation
a^2 - 10a + 9 = 0
solve it and you have a = 1 or 9 the same for b
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