The Arithmetic Mean of n numbers a 1 , a 2 , ⋯ , a n is equivalent to
n a 1 + a 2 + ⋯ + a n ,
while the Geometric Mean is equivalent to
( a 1 a 2 ⋯ a n ) n 1 .
Given that the AM and GM of two numbers are 3 4 and 1 6 respectively, find the sum of the two numbers.
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LOL, originally I had the AM and GM values mixed up. I got 16 + 30i and 16 - 30i as their values (I knew the sum but just out of curiosity).
Wow the answer is right in front of you!
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From the problem statement, we know that AM of the two numbers is 3 4 . Thus, if the numbers were a , b , then 2 a + b = 3 4
Thus, a + b = 6 8 and we are done.