Question

(x+2)^1/4 + 2=5

Answer 1

x = 79

Answer 2

Can you work that out? I got 607 by subtracting 2 and then ^4 on both sides.

Answer 3

(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

Answer 4

boom

Answer 5

Awesome, thank you.

Answer 6

But if you could write it in terms that someone in intermediate algebra could understand that would also help, haha. Thanks none-the-less.

Answer 7

Never mind, I got it.