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Using Properties of Proportion Solve for X: Sqrt(X + 1) + Sqrt(X - 1))/(Sqrt(X + 1) - Sqrt(X - 1)) = (4x - 1)/2 - ICSE Class 10 - Mathematics

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Question

Using properties of proportion solve for x:

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

Solution

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

Applying componendo and dividendo

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

`(2sqrt(x + 1))/(2sqrt(x - 1)) = (4x + 1)/(4x - 3 )`

Squaring both sides

`(x + 1)/(x - 1) = (16x^2 + 1 + 8x )/(16x^2 + 9 - 24x)`

Applying componedo and dividendo

`(x + 1 + x - 1)/(x + 1 - x + 1) = (16x^2 + 1 + 8x + 16x^2 + 9 - 24x)/(16x^2 + 1 + 8x - 16x^2 - 9 + 24x)`

`(2x)/2 = (32x^2 + 10 - 16x )/(32x - 8)`

`x = (16x^2 + 5 - 8x)/(16x - 4)`

`16x^2 - 4x = 16x^2 + 5 - 8x`

4x = 5

x = 5/4

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APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7C | Q: 11.2

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Solution Using Properties of Proportion Solve for X: Sqrt(X + 1) + Sqrt(X - 1))/(Sqrt(X + 1) - Sqrt(X - 1)) = (4x - 1)/2 Concept: Proportions.
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