Question

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Answer 1

Step-by-step explanation:

Given :-

(1/5) : (1/x) :: (1/x) :(4/5)

To find :-

Find the value of x ?

Solution :-

Method -1:-

Given that :

(1/5) : (1/x) :: (1/x) :(4/5)

Since they are in proportion then

The product of means = The product of extremes

The product of means = (1/x)×(1/x)

=> (1×1)/(x×x)

=> 1/x²

and

The product of extremes = (1/5)×(4/5)

=> (1×4)/(5×5)

=> 4/25

Now,

=> 1/x² = 4/25

=> (1/x)² = 4/25

=> 1/x = ±√(4/25)

=> 1/x = ±(2/5)

=> x = ±5/2

=> x = 5/2 or -5/2

The positive value of x = 5/2

Method -2:-

Given that :

(1/5) : (1/x) :: (1/x) :(4/5)

1/x is the mean Proportional

We know that

The mean Proportional of a and b is √(ab)

Here, a = 1/5 and b= 4/5

=> 1/x = √[(1/5)×(4/5)]

=> 1/x =√(4/25)

=> 1/x = 2/5

=> x = 5/2

Therefore, x = 5/2

Answer:-

The positive value of x for the given problem is 5/2

Used formulae:-

→ In proportion,The product of means = The product of extremes

→ The mean Proportional of a and b is √(ab)