Answer:
The solutions to the equation (x 8)² - 2 = 0 are x = 8 + sqrt(2) and x = 8 - sqrt(2).
Explanation:
First, let's rewrite your equation in the standard form:
(x 8)² - 2 = 0
=> x² - 16x + 64 - 2 = 0
=> x² - 16x + 62 = 0
Now, we can solve this quadratic equation using the quadratic formula, which is given by:
x = [-b ± sqrt(b² - 4ac)] / (2a)
In your equation, a = 1, b = -16, and c = 62. Plugging these values into the quadratic formula gives:
x = [16 ± sqrt((-16)² - 4*1*62)] / (2*1)
=> x = [16 ± sqrt(256 - 248)] / 2
=> x = [16 ± sqrt(8)] / 2
=> x = [16 ± 2sqrt(2)] / 2
=> x = 8 ± sqrt(2)