Question

1 Solve the following quadratic equations by completing the square .

Answer 1

4x² + 4bx - (a² - b²) = 0
[(2x)² + 2(2x)(b) + b²] - b² - (a² - b²) = 0
(2x + b)² - b² - a² + b² = 0
(2x + b)² - a² = 0
(2x + b)² = a²
(2x + b) = ⁺₋ a

taking (+ve)

2x + b = a
2x = (a - b)
x = (a - b)/2


taking (-ve)

2x + b = -a
2x = -(a + b)
x = -(a + b)/2

Answer 2

Given Quadratic equation

4x² + 4bx - ( a² - b² ) = 0

=> 4x² + 4bx - a² + b² = 0

=>[(2x)²+2 ×( 2x )×b + b² ]= a²

=> ( 2x + b )² = a²

=> 2x + b = ± √a²

=> 2x + b = ± a

=> 2x = -b ± a

=> x = ( -b ± a )/2

Therefore ,

x = ( -b + a )/2 Or x = (- b - a )/2

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