Question

2. Solve the following quadratic equations using quadratic formula

Answer 1

$x1,2= \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ + 12a + - \sqrt{144 {a}^{2} - 144 {a}^{2} + 144 {b}^{2} } }{72} \\ = \frac{12a + - 12b}{72} \\ x1 = \frac{a + b}{6} \\ x2 = \frac{a - b}{6}$

Answer 2

Compare given Quadratic equation

36x² -12ax + ( a² - b² ) = 0 with

Ax² + Bx + C = 0 we get ,

A = 36 , B = -12a , C = a² - b² ,

Discreminant ( D ) = B² - 4AC

= ( -12a )² - 4 × 36 × ( a² - b² )

= 144a² - 144( a² - b² )

= 144a² - 144a² + 144b²

D = 144b²

By Quadratic Formula :

x = [ -B ± √D ]/2A

= [ -( -12a ) ± √ ( 144b² ) ]/( 2 × 36 )

= [ 12a ± 12b ]/72

= [ 12( a ± b ) ]/72

= ( a ± b )/6

Therefore ,

x = ( a + b )/6 or x = ( a - b )/6

••••