Final answer:
The equation eˣ / x³ = 2x + 1 is a transcendental equation and requires numerical methods or computational tools to find an approximate solution. The solutions can be found by determining where the function f(x) = eˣ / x³ - (2x + 1) intersects the x-axis and expressing these intersection points correct to two decimal places.
Step-by-step explanation:
To solve the equation eˣ / x³ = 2x + 1, we must recognize that this is a transcendental equation and cannot be solved using algebraic methods alone. Instead, numerical methods such as Newton's method or computational tools would be required to find an approximation to the solutions.
We begin by setting up the equation to find where the function f(x) = eˣ / x³ - (2x + 1) equals zero. Since this equation does not simplifies to a convenient form for analytical solutions, we resort to an approximate method. One can use graphing calculators, software like MATLAB, or online computational tools to plot the function and find where it intersects the x-axis, which would represent the solutions to the original equation.
We then use the numerical approximation to express the solutions correct to two decimal places, as required.