SOLUTION: Find all real solutions of the following equation.
(x + 3)5 - 4(x + 3)3 = 0
x =__ (smallest solution)
x =___
x = ___ (largest solution)
i cant seem to figure out how to do
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Question 178968: Find all real solutions of the following equation.
(x + 3)5 - 4(x + 3)3 = 0
x =__ (smallest solution)
x =___
x = ___ (largest solution)
i cant seem to figure out how to do this! Help! thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.
Let
Replace each "x+3" with "z".
Factor out the GCF (note: you can avoid the substitution, but factoring is much easier to see)
Factor into by use of the difference of squares formula
, , or Set each factor equal to zero
, , or Solve for "z" in each case
, , or Plug in (remember, we want to solve for "x")
, , or Subtract 3 from both sides (for each equation)
, , or Combine like terms.
------------------------------------------
Answer:
So the solutions are , , or
Note: if you plug in any solution into the given equation and simplify, you should get . If you do this to all of the solutions, then this will verify the answer.
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