Final answer:
To solve the quadratic equation 8cos²x-10cosx+3=0, we can use the quadratic formula. The solutions are x = 3/4 and x = 1/2.
Step-by-step explanation:
To solve the quadratic equation 8cos²x-10cosx+3=0, we can use the quadratic formula. For an equation of the form ax²+bx+c=0, the quadratic formula is x = (-b ± √(b²-4ac))/(2a).
In this case, a = 8, b = -10, and c = 3. Plugging these values into the quadratic formula, we get x = (-(-10) ± √((-10)²-4(8)(3)))/(2(8)). Simplifying, we have x = (10 ± √(100-96))/16. Continuing to simplify, we have x = (10 ± √4)/16. Therefore, the two solutions are x = (10+2)/16 = 12/16 = 3/4 and x = (10-2)/16 = 8/16 = 1/2.