Question

1.
${x}^{2} - 4ax + 4 {a}^{2} - {b}^{2} = 0$
solve for x
2.
$9 {x}^{2} - 6 {a}^{2} x + ( {a}^{4} - {b}^{4} ) = 0$
solve for x
these 2 questions are separate

Answer 1

-(1) x² - 4ax + (4a² - b²)

=> x² - 4ax + [(2a - b)(2a + b)]

=> x² - (2a - b + b +2a) + [(2a - b)(2a + b)]

=> x² - (2a - b)x - (2a + b)x + [ (2a -b)(2a+b)]

=> x[x - (2a -b)] - (2a +b) [ x - (2a -b)]

=> [x - (2a - b)] [(x - (2a +b)]

=> x = (2a - b)

and,

x = (2a+b)



----(2)

9x² - 6a²x + (a⁴ - b⁴)

=> 9x² - 6a²x + (a² - b²)(a² + b²)

=> 9x² - [3(a² - b²) + 3(a² + b²)]x + (a² - b²)(a² + b²)

=> 9x² - 3(a² - b²)x - 3(a² + b²)x + (a² - b²)(a² + b²)

=> 3x[3x - (a² - b²) ] - (a² + b²)[3x - (a² - b²)]

=> [3x - (a² - b²)] [3x - (a² + b²)]

=> x = (a² - b²)/3

AND,

x = (a² + b²)/3