Question

If 2, x and 8 are in continued proportion, then x

Answer 1

Answer:

2,x,8 are in continued prop

then

x2=8 x 2

=16

x=4

Step-by-step explanation:

Answer 2

The value of x = 4

Given :

2 , x , 8 are in continued proportion

To find :

The value of x

Solution :

Step 1 of 2 :

Form the equation

Here it is given that 2 , x , 8 are in continued proportion

Thus we get

2 : x = x : 8

Step 2 of 2 :

Find the value of x

$\displaystyle \sf{ 2 : x = x : 8 }$

$\displaystyle \sf{ \implies \frac{2}{x} = \frac{x}{8} }$

$\displaystyle \sf{ \implies {x}^{2} = 2 \times 8}$

$\displaystyle \sf{ \implies x = \sqrt{2 \times 8} }$

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

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

$\displaystyle \sf{ \implies x = 2 \times 2}$

$\displaystyle \sf{ \implies x = 4}$

Hence the required value of x = 4

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