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Find two numbers whose arithmetic mean i...

Find two numbers whose arithmetic mean is 34 and the geometric mean is 16.

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The correct Answer is:
64 and 4
Let the two numbers be a and b. Then,
A.M.=34
`rArr(a+b)/2=34` or a+b=68
G.M=16
`rArrsqrt(ab)=16` or ab=256
`therefore(a-b)^(2)=(a+b)^(2)-4ab`
or `(a-b)^(2)=(68)^(2)-4xx256=3600`
or a-b=60 (2)
On solving (1) and (2), we get a= 64 and b=4. Hence, the required numbers are 64 and 4.
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