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 $s$.

Guest Jun 30, 2018

#1**+1 **

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

#1**+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