easy one !!!!

Algebra Level 2

The Arithmetic Mean of n n numbers a 1 , a 2 , , a n a_{1},a_{2},\cdots,a_{n} is equivalent to

a 1 + a 2 + + a n n , \frac{a_{1}+a_{2}+\cdots+a_{n}}{n},

while the Geometric Mean is equivalent to

( a 1 a 2 a n ) 1 n . (a_{1}a_{2}\cdots a_{n})^{\frac{1}{n}}.

Given that the AM and GM of two numbers are 34 34 and 16 16 respectively, find the sum of the two numbers.


The answer is 68.

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2 solutions

Daniel Liu
Jun 28, 2014

From the problem statement, we know that AM of the two numbers is 34 34 . Thus, if the numbers were a , b a,b , then a + b 2 = 34 \dfrac{a+b}{2}=34

Thus, a + b = 68 a+b=\boxed{68} and we are done.

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).

Sharky Kesa - 6 years, 11 months ago
William Isoroku
Aug 29, 2014

Wow the answer is right in front of you!

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