Solve the quadratic equation 2x^2 - 4x + 1 = 0

Answer 1

Using the quadratic formula, we can solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 2, b = -4, and c = 1. Substituting in these values, we get:

x = (-(-4) ± sqrt((-4)^2 - 4(2)(1))) / (2 * 2)
x = (4 ± sqrt(16 - 8)) / 4
x = (4 ± sqrt(8)) / 4
x = (4 ± 2sqrt(2)) / 4

Therefore, the solutions to the quadratic equation are x = (4 + 2sqrt(2)) / 4 and x = (4 - 2sqrt(2)) / 4, which simplify to x = 1 + sqrt(2) / 2 and x = 1 - sqrt(2) / 2, respectively.