geometry

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Is it possible for the geometric mean and the arithmetic meam of two numbers,a and b, to be the same? explain.
can you help me answer this question? thank you

• geometry -

Assuming it is possible that the arithmetic mean and geometric mean of two numbers to be the same, and let
one of the numbers be 10, and the other one, x.

We want to find x such that
(10+x)/2 = sqrt(10x)
squre both sides
(x²+20x+100)/4 = 10x
x²+20x+100 = 40x
x²-20x+100 = 0
Factor:
(x-10)²=0
Therefore the other number is 10.

Corollary:
Try two equal numbers:
(x+x)/2=x
sqrt(x*x) = x
therefore if two numbers are equal, their geometric and arithmetic means are equal.

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