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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 - 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

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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(D) | Q: 21 | Page no. 102

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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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