Find the sum of the coordinates of the intersection points of the graphs of the functions y = 2x-4 and y = √ (x ^ 2 – x + 4).

To find a solution to the problem, we will compose and solve a system of these equations:

System of equations:

y = 2x – 4;

y = √ (x ^ 2 – x + 4).

We solve using the substitution method. Substitute the expression from the second into the first equation instead of y:

2x – 4 = √ (x ^ 2 – x + 4);

4x ^ 2 – 16x + 16 = x ^ 2 – x + 4;

3x ^ 2 – 15x + 12 = 0.

We calculate the discriminant of the equation:

D = 15 ^ 2 – 4 * 3 * 12 = 81.

x1 = (15 + 9) / 6 = 4;

x2 = (15 – 9) / 6 = 1.

y1 = 2 * 4 – 4 = 4;

y2 = 2 * 1 – 4 = -2.

(4; 1) and (4; -2).

We are looking for the sum of the coordinates of the points:

(8; -1).