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Using Properties of Proportion Solve for X: (3x + Sqrt(9x^2 - 5))/(3x - Sqrt(9x^2 - 5)) = 5 - Mathematics

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Question

Using properties of proportion solve for x:

`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`

Solution

`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`

Applying componendo and dividendo

`(3x + sqrt(9x^2 - 5) + 3x - sqrt(9x^2 - 5))/(3x sqrt(9x^2 - 5) - 3x + sqrt(9x^2 - 5)) = (5 + 1)/(5 - 1)`

`(6x)/(2sqrt(9x^2 - 5)) = 6/4`

`x/sqrt(9x^2 - 5) = 1/2`

Squaring both sides

`x^2/(9x^2 - 5) = 1/4`

`4x^2 - 9x^2 - 5`

`5x^2 = 5`

`5x^2  = 5`

`x^2 = 1`

x = 1

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(C) | Q: 11.3 | Page no. 102
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Using Properties of Proportion Solve for X: (3x + Sqrt(9x^2 - 5))/(3x - Sqrt(9x^2 - 5)) = 5 Concept: Concept of Proportion.
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