Final answer:
To find the value of x for the rectangular box with given dimensions and volume, we set up and solve a cubic equation based on the formula for the volume of a rectangular box. After solving the equation, we determine that the only valid solution for x is 4.
Step-by-step explanation:
To find the value of x for which a rectangular box with edges x, (x-3), and (x+4) has a volume of 8x, we can set up an equation using the formula for the volume of a rectangular box, which is the product of its length, width, and height:
V = l × w × h
Here, V = 8x, and the edges are x, (x-3), and (x+4). So we have:
8x = x(x-3)(x+4)
To find x, we solve the cubic equation:
- 8x = x × (x2 + x - 12)
- 8 = x2 + x - 12
- x2 + x - 20 = 0
- (x+5)(x-4) = 0
- So, x = -5 or x = 4
However, since an edge of a box cannot be negative, we discard x = -5, and the answer is x = 4.