Q. 104.8( 6 Votes )

If AM and GM of two positive numbers a and b are 10 and 8 respectively, find the numbers.

Answer :


GM = √ab


Given AM = 10, GM = 8.



a + b = 20


a = 20–b



20b – b2 = 64


b2 – 20b + 64 = 0


b2 – 16b – 4b + 64 = 0


b(b – 16) – 4(b – 16) = 0


b = 4 or b = 16


If b = 4 then a = 16


If b = 16 then a = 4.


Hence, the numbers are 4 and 16.


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