SOLUTION: Find the real solutions of the given equation. Use a calculator to express solutions rounded to two decimal places. x^(2/3) + 4x^(1/3) + 2 = 0

Algebra ->  Equations -> SOLUTION: Find the real solutions of the given equation. Use a calculator to express solutions rounded to two decimal places. x^(2/3) + 4x^(1/3) + 2 = 0       Log On


   

Question 1208848: Find the real solutions of the given equation. Use a calculator to express solutions rounded to two decimal places.
x^(2/3) + 4x^(1/3) + 2 = 0

Found 3 solutions by josgarithmetic, MathTherapy, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
try something like t=x%5E%281%2F3%29 and then you have (t equals x to the one-third power)
t%5E2%2B4t%2B2=0

t=%28-4%2B-+sqrt%284%5E2-4%2A2%29%29%2F2
t=%28-4%2B-+sqrt%288%29%29%2F2
t=%28-4%2B-+2%2Asqrt%282%29%29%2F2
t=-2%2B-+sqrt%282%29

Two things to do now.
x%5E%281%2F3%29=-2-sqrt%282%29
The other possible x
x%5E%281%2F3%29=-2%2Bsqrt%282%29

Cube both sides for each, to find x.

Answer by MathTherapy(10552) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are two solutions, using the path shown by tutor @josgarithmetic.

x%5E%281%2F3%29=-2%2Bsqrt%282%29 and x%5E%281%2F3%29=-2-sqrt%282%29

Cubing each of those values gives the two (approximate) solutions x = -0.20101 and x - -39.79899.

The graphing feature of this web site can't handle an equation like that. Verify the solutions by making a graph using a calculator like the TI-84, or using the graphing utility at geogebra.org.