Answer:
Step-by-step explanation:
Replace m - 2 with x. Then we have x^2 - 4x + 2 = 0.
Completing the square, we get x^2 - 4x + 4 - 4 + 2 = 0, or
x^2 - 4x + 4 - 2 = 0, or
(x - 2)^2 - 2 = 0, or (x - 2)^2 = 2
Solve for x: Take the square root of both sides. Then:
x - 2 = ±√2 and x = 2 + √2 and x = 2 - √2
But x = m - 2; therefore, x = m - 2 = 2 - √2. Solving for m, we get
m = 4 - √2.
Also: m - 2 = 2 + √2 leads to m = 4 + √2.
The given equation is true for these two values of m.
