Posted by **mike** on Thursday, February 10, 2011 at 8:58pm.

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 -
**MathMate**, Thursday, February 10, 2011 at 10:23pm
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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