Answer:
Step-by-step explanation:
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When you cut off for squares of x side length, the area of the base of the box is [10 - 2x]^2 and the height ot the box is x, then the volumen of the box is:
(10 - 2x)^2 * x = 48
(100 - 40x + 4x^2)*x = 48
100x - 40x^2 + 4x^3 = 48
4x^3 - 40x^2 + 100x - 48 = 0
x^3 - 10x^2 + 25x - 12 = 0
Using Ruffini you can get 3 as a solutio:
3^3 - 10(3^2) + 25(3) - 12 = 27 - 90 + 75 - 12 = 0
Factoring you get (x - 3) (x^2 -7x + 4) = 0
Then, you can apply the quadratic formula to x^2 -7x + 4 to find the other two roots.
They are x = 0.6277 and x = 6.3723.
x = 6.32723 is not valid because 10 - 2x < 0.
Then there are two real solutcions for the side of the squate: 3 and 0.6277 (althoug the second one is a very low box)
