Question

If arithmetic and geometric mean of two positive numbers are 5 and 3 then numbers

Answer 1

The two positive numbers are 1 and 9.

Step-by-step explanation:

Given : If arithmetic and geometric mean of two positive numbers are 5 and 3.

To find : The numbers ?

Solution :

Let the two numbers be 'a' and 'b'.

The arithmetic mean of two positive numbers is $A.M=\frac{a+b}{2}$

i.e. $\frac{a+b}{2}=5$

$a+b=10$ .....(1)

The geometric mean of two positive numbers is $G.M=\sqrt{ab}$

i.e. $\sqrt{ab}=3$

$ab=9$  ....(2)

Solving (1) and (2),

Substitute the value of a from (1) in (2),

$(10-b)b=9$

$10b-b^2=9$

$b^2-10b+9=0$

$b^2-9b-b+9=0$

$b(b-9)-1(b-9)=0$

$(b-9)(b-1)=0$

$b=9,1$

Substitute in (1),

When b=9,

$a+9=10$

$a=1$

When b=1,

$a+1=10$

$a=9$

#Learn more

The arithmetic mean of two numbers be A and geometric mean be G then the numbers will be

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