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If A.M. of two numbers is 15/2 and their G.M. is 6, then find the two numbers.(a) 6 and 8(b) 12 and 3(c) 24 and 6(d) 27 and 3I got this question in unit test.I want to ask this question from Relationship Between A.M. and G.M. topic in section Sequences and Series of Mathematics – Class 11

Answer»

The correct OPTION is (b) 12 and 3

The explanation: We know, A.M. of two NUMBERS a and b is (a + b)/2

=> (a + b)/2 = 15/2 => a + b = 15.

Also, G.M. of two numbers a and b is \(\sqrt{ab}\)

=> \(\sqrt{ab}\) = 6 => ab = 36.

=> a(15-a) = 36 => a=3 or 12.

For a=3, b=12.

For a=12, b=3.

So, the two numbers are 3 and 12.


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