Expert: Paul Klarreich - 9/4/2009

Question
How would i begin to solve this: The arithmetic mean of 2 numbers is 12. their geometric mean is 8. find the sum of the square roots of the 2 numbers

Answer
Questioner: miranda
Country: United States
Category: Advanced Math
Private: No
Subject: pre-calculus
Question: How would i begin to solve this: The arithmetic mean of 2 numbers is 12. their geometric mean is 8. find the sum of the square roots of the 2 numbers
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Hi, Miranda,

Here is how you begin:

A. Determine what the variables are, such as:

The first number
The second number

B. Give them names.  

Let x = The first number
Let y = The second number

C. Look up the meanings of vocabulary terms.  If you don't know what the words mean, you can't do anything.  Such as:

The arithmetic mean of x and y is  (x + y)/2

The geometric mean of x and y is  sqrt(xy).

Next write the symbolic form of the sentences, such as:

The arithmetic mean of 2 numbers is 12.

becomes

(x + y)/2 = 12

their geometric mean is 8

sqrt(xy) = 8

Now you are started.
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Hints for finishing up:

1. You don't have to actually find x,y.

2. Let SUM = sqrt(x) + sqrt(y), which you have to find.

compute  SUM^2 = (sqrt(x) + sqrt(y))^2 and relate the result to the stuff above.  If you get stuck, send me what you did and I'll see what I can do.