Maths question?

Question

 solve:
square root(4x - 3) + square root(2x +3) = 6    

 

 

 

Answer 1

The equation is √(4x - 3) + √(2x + 3) = 6.

Square on both sides.

[√(4x - 3) + √(2x + 3)] ² = 6²

(4x - 3) + (2x + 3) + 2√(4x - 3)√(2x + 3) = 36

6x + 2√[(4x - 3)(2x + 3)] = 36

3x + √[(4x - 3)(2x + 3)] = 18

√[(4x - 3)(2x + 3)] = 18 - 3x

(4x - 3)(2x + 3) = (18 - 3x)²

8x² + 6x - 9 = 324 + 9x² - 108x

x² - 114x + 333 = 0

x² - 111x - 3x + 333 = 0

x(x - 111) - 3(x - 111) = 0

(x - 3)(x - 111) = 0

x = 3 or x = 111

The value of x = 111 does not satisfy the original equation.

The solution is 3.