Question

The geometric mean is 6. The smaller number is one third of the larger. What are the two numbers​

Answer 1

Step-by-step explanation:

we know

geometric mean

of x&y

√x.y =6

Answer 2

The two numbers are 2√3 and 6√3

Given :

• The geometric mean is 6

• The smaller number is one third of the larger

To find :

The two numbers

Solution :

Step 1 of 2 :

Form the equation to find the two numbers

Here it is given that for the two numbers the smaller number is one third of the larger

Let smaller number = x

∴ The larger number = 3x

Now it is given that the geometric mean is 6

Thus we get ,

$\displaystyle \sf \sqrt{3x.x} = 6$

Step 2 of 2 :

Find the two numbers

$\displaystyle \sf \sqrt{3x.x} = 6$

$\displaystyle \sf{ \implies } \sqrt{3 {x}^{2} } = 6$

$\displaystyle \sf{ \implies }x \sqrt{3} = 6$

$\displaystyle \sf{ \implies }x = \frac{6}{ \sqrt{3} }$

$\displaystyle \sf{ \implies }x = \frac{6 \sqrt{3} }{ \sqrt{3} \times \sqrt{3} }$

$\displaystyle \sf{ \implies }x = \frac{6 \sqrt{3} }{ 3 }$

$\displaystyle \sf{ \implies }x = 2 \sqrt{3}$

The smaller number = 2√3

The larger number = 6√3

Hence two numbers are 2√3 and 6√3

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