Find the sum of the abscissas of the intersection points of the graphs of the function y = 7x-8 and y = x².

Find the coordinates of the intersection points of the given functions.

To do this, we equate the right-hand sides of the formulas and solve the equation.

x² = 7x – 8.

We transform the equation: we transfer all the terms to the left side of the equation and write the polynomial in the standard form.

We solve the quadratic equation using the formula through the discriminant.

x² – 7x + 8 = 0.

D = 49 – 32 = 17.

√D = √17.

x1,2 = (7 ± √17) / 2.

x1 = 3.5 + √17 / 2 and x2 = 3.5 – √17 / 2 are the abscissas of the intersection points of the graphs.

x1 + x2 = 3.5 + √17 / 2 + 3.5 – √17 / 2 = 3.5 + 3.5 = 7.

Answer: 7.