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.
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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