Final answer:
To find the positive root of the given equation using the Newton-Raphson method, start with an initial guess for the root and use the iterative formula to approximate the root.
Step-by-step explanation:
The given equation is f(x) = 2x³ - 3x - 6 = 0. To find the positive root using Newton-Raphson method, we start with an initial guess for the root, let's say x0. We can then use the formula xn+1 = xn - f(xn)/f'(xn) to iteratively approximate the root.
Let's use x0 = 1:
x1 = 1 - (2(1)³ - 3(1) - 6)/(6(1)² - 3)
Keep iterating the formula until the value of xn+1 aligns with the value of xn, correct to five decimal places.