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The "volume" equation is
x*(x+1)*(x^2+1) = 120 cubic feet.
One solution can be easily guessed: x = 3.
Indeed, 3*(3+1)*(3^2+1) = 3*4*10 = 12*10 = 120.
Next, notice that the function x*(x+1)*(x^2+1) is monotonically increased.
It means that x = 3 is the UNIQUE solution to the "volume" equation, and THERE IS NO other real solution.
ANSWER. Under given conditions, the unique set of the dimensions of the tank is 3 ft, 4 ft, and 10 ft.
Solved.
