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# A cube of edge length s

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

Dec 5, 2020

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

Surface area            =    6s2

Volume                     =     s3

Twice the edge length    =    2s

Set up the equality                                   s3 + 2s  =  6s2

Rearrange terms                             s3 – 6s2 + 2s  =  0

Factor out an s                            s • (s2 – 6s + 2)  =  0

Divide both sides by s                          s2 – 6s + 2  =  0

I couldn't factor that so

used the binomial formula

The answers for s I got were           s = 3 + sqrt(7)  and  s = 3 – sqrt(7)

Adding them together                      Their sum is   6

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Dec 5, 2020
edited by Guest  Dec 5, 2020