Question

If the arithmetic mean of two numbers is 15 and their geometric mean is 9, find the numbers?

Answer 1

Let a and b the number


so ,

a+ b /2 = 15

ab =30 ---------------------1


now GM =√ab

=> ✓ ab = 9

ab = 81 ----------------------2


from the equation 1 and 2 we have


(a-b )² =( a+ b) ² -4ab


( a- b )² = 900 - 4× 81

( a-b )² = 900 - 324

( a- b )² = 576

( a- b ) = 24 ------------------(3)



from equation 1 and 3 we get


a + b = 30
a - b = 24

a = 27


b = 3


hope it help you !!!

thanks !!

Ranjan kumar


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