Question

X square minus 2 mx plus m square minus n square is equal to zero. Solve by quadratic equations formula

Answer 1

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

Answer 2

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 3

To solve the equation X^2 - 2mx + m^2 - n^2 = 0 using the quadratic formula, we can follow these steps:

Step 1: Identify the coefficients of the quadratic equation In this case, the coefficients are: a = 1 (coefficient of X^2) b = -2m (coefficient of X) c = m^2 - n^2

Step 2: Apply the quadratic formula The quadratic formula is given by: X = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c into the formula, we get: X = (-(-2m) ± √((-2m)^2 - 4(1)(m^2 - n^2))) / (2(1))

Simplifying further: X = (2m ± √(4m^2 - 4(m^2 - n^2))) / 2 X = (2m ± √(4m^2 - 4m^2 + 4n^2)) / 2 X = (2m ± √(4n^2)) / 2 X = (2m ± 2n) / 2

Step 3: Simplify the expression We can simplify the expression by canceling out the common factor of 2: X = m ± n

Therefore, the solutions for the equation X^2 - 2mx + m^2 - n^2 = 0 are X = m + n and X = m - n.