Question

${x}^{2} - 2ax + ( {a}^{2} - {b}^{2}) = 0$
solve for x

Answer 1

x² - 2ax + (a² - b²)

=> x² - 2ax + (a - b)(a + b)

=> x² - (a - b + a + b)x + (a - b)(a + b)

=> x² - (a - b)x - (a + b)x + (a - b)(a + b)

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

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

=> x = (a - b)

AND,

x = (a + b)