Final answer:
The sum of the solutions to the given equation is k(4a+b), where k is a constant. The value of k is 1/8.
Step-by-step explanation:
The given equation is a quadratic equation of the form ax² + bx + c = 0, with a = 64, b = -(16a+4b), and c = ab. We need to find the sum of the solutions to the equation in terms of the constants a and b. To do this, we can use the quadratic formula.
The quadratic formula is: x = (-b ± √(b² - 4ac)) / (2a). Substituting the values of a, b, and c into the formula, we get:
x = (-(16a+4b) ± √((16a+4b)² - 4(64)(ab))) / (2*64)
Simplifying further, we have:
x = (-(16a+4b) ± √((16a+4b)² - 256ab)) / 128
The sum of the solutions is given by the expression k(4a+b), where k is a constant. Comparing this expression with the above equation, we can see that k = 1/8. Therefore, the value of k is b. 1/8.