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.

## Answer this Question

## Related Questions

- geometry/help - Is it possible for the geometric mean and the arithmetic meam ...
- math - What is the difference between geometric mean and arithmetic mean? ...
- ALGEBRA - the arithmetic mean of two numbers exceeds their geometric mean by two...
- geometric mean - The geometric mean of two postitive numbers a and b is sqrt(ab...
- ALGEBRA - the arithmetic mean of two numbers exceeds their geometric mean by two...
- math - The arithmetic mean of two numbers is 9 and their geometric mean is 3&#...
- Geometry-8th gr - The geometric mean x of two numbers is the positive value of x...
- Math - Determine whether this sequence is arithmetic or geometric. Find the next...
- Math - Determine whether each sequence is arithmetic of geometric. Find the next...
- Math *URGENT - Please give the answers and solutions for each. 1.If the second ...

More Related Questions