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  • If A.M. of two positive number a and b is 5 and their G.M. is 3, then numbers a and b areOption: 1 2,8<str

If A.M. of two positive number a and b is 5 and their G.M. is 3, then numbers a and b are

Option: 1

2,8


Option: 2

3,7


Option: 3

1,9


Option: 4

1,10


Answers (1)

best_answer

A.M. = 5

\\\frac{a+b}{2}= 5\\ \Rightarrow a+b=10.....(i)

G.M. = 3

\\\sqrt{ab}= 3\\ \Rightarrow ab=9.....(ii)

Now 

\\(a-b)^2 = (a+b)^2 - 4ab = 100 - 36 = 64\\ \Rightarrow (a-b)=\pm 8......(iii)

From (i) and (iii)

(a = 9, b = 1) or (a = 1, b = 9)

Posted by

avinash.dongre

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