a) (x - 2)^2 + (x - 2)^2 = 5

1 answer

Simplifying the equation:

(x - 2)^2 + (x - 2)^2 = 5
2(x - 2)^2 = 5
(x - 2)^2 = 5/2

Taking the square root of both sides:

√((x - 2)^2) = √(5/2)
|x - 2| = √(5/2)

The absolute value represents two possibilities:

1) x - 2 = √(5/2)
x = √(5/2) + 2

2) x - 2 = -√(5/2)
x = -√(5/2) + 2

Therefore, the solutions to the equation are x = √(5/2) + 2 and x = -√(5/2) + 2.