What are the 2 numbers with GM= 4 and HM=16/5?

Expert Answers

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Let the two numbers be A and B. Now it is given that their GM is 4.

This gives us sqrt (A*B) = 4

=> AB = 4^2 = 16

We also know that their HM is 16/5, so 2*AB / (A+B) = 16/5

=> 2*AB / (A+B) = 2*16 / (A+B) = 16/5

=> (A + B) = 2*16*5/16 = 10

=> A + B = 10

=> A = 10 - B

AB = (10 - B)*B = 16

=> 10B - B^2 = 16

=> B^2 - 10B + 16 = 0

=> B^2 - 8B - 2B + 16 = 0

=> B( B - 8) - 2(B -8) = 0

=> ( B - 2)(B - 8) = 0

=> B is 2 and 8

=> A is 8 and 2

The two numbers are 8 and 2.

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