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Question

A cube of edge length s > 0 has the property that its surface area is equal to the sum of its volume and five times its edge length. Compute the sum of all possible values of s. FIGURE

Accepted Answer

The volume of the cube is s^3 and its surface area is 6s^2, so we have 6s^2=s^3+5s, or 0=s^3-6s^2+5s=s(s-1)(s-5). So, the two nonzero possibilities for s are 1 and 5. Their sum is 6.