anonymous
  • anonymous
(x+2)^1/4 + 2=5
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
x = 79
anonymous
  • anonymous
Can you work that out? I got 607 by subtracting 2 and then ^4 on both sides.
anonymous
  • anonymous
(x+2)^(1/4)+2 = 5 Subtract 2 from both sides: (x+2)^(1/4) = 3 Let x+2 = r (cos(theta)+i sin(theta)) and write 3 in phasor form: (r (cos(theta)+i sin(theta)))^(1/4) = 3 (cos(0)+i sin(0)) Use de Moivre's theorem: r^(1/4) (cos(theta/4)+i sin(theta/4)) = 3 (cos(0)+i sin(0)) Equating moduli and arguments gives: r^(1/4) = 3 and theta/4 = 2 pi k Solving these equations and selecting the 1 distinct solutions gives: r = 81 and theta_1 = 0 Then the equation (x+2)^(1/4) = 3 has the solutions: x+2 = 81 Subtract 2 from both sides: x = 79 Now test that this solution is appropriate by substitution into the original equation: Check the solution x = 79: (x+2)^(1/4)+2 => 2+(2+79)^(1/4) = 5 So the solution is correct. Thus, the solution is: x = 79

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anonymous
  • anonymous
boom
anonymous
  • anonymous
Awesome, thank you.
anonymous
  • anonymous
But if you could write it in terms that someone in intermediate algebra could understand that would also help, haha. Thanks none-the-less.
anonymous
  • anonymous
Never mind, I got it.

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