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  4. The A.M. of two numbers is 34 and GM is 16 , the numbers are-

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Q. The A.M. of two numbers is 34 and $GM$ is 16 , the numbers are-

Sequences and Series

Solution:

Let the numbers are $a$ and $b$.
A.M. of $a$ and $b=\frac{a+b}{2}=34 $ (Given)
$\therefore a+b=68$
G.M. of $a$ and $b=\sqrt{a b}=16$ (Given)
$\therefore a b=256$
$a+b=68$ and $a b=256$
$\therefore a=64, b=4 $
Numbers are 64 and 4.