X square minus 2 mx plus m square minus n square is equal to zero.

Solve by quadratic equations formula

X² - 2mx + m² - n² = 0

(x - m) ² - n² = o

(x - m - n) (x - m + n) = 0

x - m - n = 0 ⇒ x₁ = m + n

x - m + n = 0 ⇒ x₂ = m - n

Решим через дискриминант

a = 1

b = - 2m

c = m² - n²

D = b² - 4ac

D = ( - 2m) ² - 4 (1) (m² - n²)

D = 4m² - 4m² + 4n²

D = 4n²

x = ( - b ± √D) / 2a

x = [ - ( - 2m) ± √4n²] / 2

x = (2m ± 2n) / 2 = 2 (m ± n) / 2 = m ± n

x1 = m + n

x2 = m - n