# Solve the Following Equation - Algebra

Sum

Solve the following equation.
[sqrt( 4x + 1) + sqrt( x + 3 )]/[sqrt( 4x + 1 ) - sqrt( x+3 )]=4/1

#### Solution

[sqrt( 4x + 1) + sqrt( x + 3 )]/[sqrt( 4x + 1 ) - sqrt( x+3 )]=4/1
Applying componendo and dividendo, we get
{[sqrt( 4x + 1) + sqrt( x + 3 )] + [sqrt( 4x + 1 ) - sqrt( x+3 )]} /{[sqrt( 4x + 1) + sqrt( x + 3 )] - [sqrt( 4x + 1 ) - sqrt( x+3 )]}=4/1

⇒ (2sqrt[4x+1])/ (2sqrt[x + 3]) = 5/3
⇒ sqrt[4x+1]/sqrt[x + 3] = 5/3
Squaring on both sides, we get
(4x + 1)/(x +3) = (5/3)^2 = 25/9

⇒ 36x +9 = 25x + 75
⇒ 36x - 25x = 75 - 9
⇒ 11x = 66
⇒ x = 6
Thus, the solution of the given equation is x = 6.

Concept: Application of Properties of Equal Ratios
Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 4 Ratio and Proportion
Practice Set 4.3 | Q 4.4 | Page 70