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 Sep 22, 2019
edited by SoulSlayer615  Oct 23, 2019
 #1
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Solve for r:
1/(r^3 + 7) - 7 = -r^3/(r^3 + 7)

Multiply both sides by r^3 + 7:
1 - 7 (r^3 + 7) = -r^3

Expand out terms of the left hand side:
-7 r^3 - 48 = -r^3

Add r^3 + 48 to both sides:
-6 r^3 = 48

Divide both sides by -6:
r^3 = -8

Taking cube roots gives 2 (-1)^(1/3) times the third roots of unity:

 r = -2     or     r = 2 (-1)^(1/3)     or     r = -2 (-1)^(2/3)

 Sep 22, 2019

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