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# Using Properties of Proportion, Solve for X. Given that X is Positive: (2x + Sqrt(4x^2 -1))/(2x - Sqrt(4x^2 - 1)) = 4 - ICSE Class 10 - Mathematics

#### Question

Using properties of proportion, solve for x. Given that x is positive:

(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4

#### Solution

(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4

=> (2x + sqrt(4x^2 -1) + 2x  - sqrt(4x^2 - 1))/(2x + sqrt(4x^2 - 1) - 2x +  sqrt(4x^2 - 1)) = (4+1)/(4-1)      (By componendo dividendo)

=> (4x)/(2sqrt(4x^2 -1)) = 5/3

=> (2x)/(sqrt(4x^2 -1)) = 5/3

=> (4x^2)/(4x^2 -1) = 25/9    (squaring both sides)

=>(4x^2 - 4x^2 + 1)/(4x^2 -1) = (25-9)/9    (By dividendo)

=> 1/(4x^2 -1)  = 16/9

=> 9 = 64x^2 - 16

=> 64x^2 = 25

=> x^2 = 25/64

=> x = +- 5/8

=> x = 5/8   (x is positive)

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Solution Using Properties of Proportion, Solve for X. Given that X is Positive: (2x + Sqrt(4x^2 -1))/(2x - Sqrt(4x^2 - 1)) = 4 Concept: Proportions.
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