Question

g.m of the number 9, x, 27, 18 find the valve of x​

Answer 1

Answer:

24

Step-by-step explanation:

Answer 2

The value of x is 24

Correct question : GM of the numbers 9 , x , 27 is 18. Find the value of x

Given :

GM of the numbers 9 , x , 27 is 18.

To find :

The value of x

Formula Used :

For the given set of n numbers a₁ , a₂ , a₃ , a₄ , . . . , aₙ

The geometric mean of the numbers

$\displaystyle \sf = \sqrt[n]{a_1 \times a_2 \times a_3 \times a_4 \times .... \times a_n }$

Solution :

Step 1 of 2 :

Form the equation to find the value of x

Here it is given that GM of the numbers 9 , x , 27 is 18.

So by the given condition is

$\displaystyle \sf \sqrt[3]{9 \times x \times 27} = 18$

Step 2 of 2 :

Find the value of x

$\displaystyle \sf \sqrt[3]{9 \times x \times 27} = 18$

$\displaystyle \sf{ \implies }243x = {18}^{3}$

$\displaystyle \sf{ \implies }243x = 5832$

$\displaystyle \sf{ \implies }x = \frac{5832 }{243}$

$\displaystyle \sf{ \implies }x = 24$

Hence the required value of x = 24

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