Question

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


Solve by quadratic equations formula

Answer 1

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

Answer 2

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