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Using Componendo And Dividendo Find the Value of X (Sqrt(3x + 4) + Sqrt(3x - 5))/(Sqrt(3x + 5) - Sqrt(3x - 5)) = 9 - ICSE Class 10 - Mathematics

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Question

Using componendo and dividendo find the value of x

`(sqrt(3x + 4) + sqrt(3x - 5))/(sqrt(3x + 5) - sqrt(3x - 5)) = 9`

Solution

`(sqrt(3x + 4) + sqrt(3x - 5))/(sqrt(3x + 5) - sqrt(3x - 5)) = 9/1`

Applying componendo and dividendo we have

`(sqrt(3x + 1) + sqrt(3x - 5) + sqrt(3x + 4) - sqrt(3x - 5))/(sqrt(3x + 4) + sqrt(3x - 5) - sqrt(3x + 4) + sqrt(3x - 5)) = (9 + 1)/(9 - 1)`

`=> (2sqrt(3x + 4))/(2sqrt(3x - 5)) = 5/4`

Squaring both sides we have

`(3x + 4)/(3x - 5) = 25/16`

`=> 16(3x + 4) = 25(3x - 5)`

`=> 48x - 64 = 75x - 125`

`=> 75x - 48x = 64 + 125`

=> 27x = 189

=> x = 189/27

=> x = 7

  Is there an error in this question or solution?

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.7D | Q: 25

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Solution Using Componendo And Dividendo Find the Value of X (Sqrt(3x + 4) + Sqrt(3x - 5))/(Sqrt(3x + 5) - Sqrt(3x - 5)) = 9 Concept: Componendo and Dividendo Properties.
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