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Using Properties of Proportion Solve for X (Sqrt(X + 5) + Sqrt(X - 16))/(Sqrt(X + 5) - Sqrt(X - 16)) = 7/3 - Mathematics

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Question

Using properties of proportion solve for x 

`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`

Solution

`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`

Applying componendo and dividendo

`(sqrt(x + 5)+ sqrt(x - 16) + sqrt(x + 5) - sqrt(x - 16))/(sqrt(x + 5)+sqrt(x - 16) - sqrt(x + 5) + sqrt(x -16)) = (7 + 3)/(7 - 3)`

`(2sqrt(x + 5))/(2sqrt(x - 16)) = 10/4`

`sqrt(x + 5)/sqrt(x - 16) = 5/2`

Squaring both sides

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

4x + 20 = 25x - 400

21x = 420

`x = 420/21 = 20`

  Is there an error in this question or solution?
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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: 11.1 | Page no. 102
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Using Properties of Proportion Solve for X (Sqrt(X + 5) + Sqrt(X - 16))/(Sqrt(X + 5) - Sqrt(X - 16)) = 7/3 Concept: Proportions.
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