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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 five times its edge length. Compute the sum of all possible values of $s$.

 

 

 Jun 30, 2018

Best Answer 

 #1
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6S^2 =S^3+ 5S, solve for S
6 S^2 = S^3 + 5 S

Subtract S^3 + 5 S from both sides:
-S^3 + 6 S^2 - 5 S = 0

The left hand side factors into a product with four terms:
-S (S - 5) (S - 1) = 0

Multiply both sides by -1:
S (S - 5) (S - 1) = 0

Split into three equations:
S - 5 = 0 or S - 1 = 0 or S = 0

Add 5 to both sides:
S = 5 or S - 1 = 0 or S = 0

Add 1 to both sides:

 S = 5   or    S = 1     Sum= 1  + 5 = 6

 Jun 30, 2018
 #1
avatar
+1
Best Answer

6S^2 =S^3+ 5S, solve for S
6 S^2 = S^3 + 5 S

Subtract S^3 + 5 S from both sides:
-S^3 + 6 S^2 - 5 S = 0

The left hand side factors into a product with four terms:
-S (S - 5) (S - 1) = 0

Multiply both sides by -1:
S (S - 5) (S - 1) = 0

Split into three equations:
S - 5 = 0 or S - 1 = 0 or S = 0

Add 5 to both sides:
S = 5 or S - 1 = 0 or S = 0

Add 1 to both sides:

 S = 5   or    S = 1     Sum= 1  + 5 = 6

Guest Jun 30, 2018

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