SOLUTION: 1.) Find the solutions of the equation. I already subuted u for x^(2/3) then i got a quadratic equation 3u^2 + 5u - 2=0 and i got u = 1/3 and -2 and i have to sub somethin

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1.) Find the solutions of the equation. I already subuted u for x^(2/3) then i got a quadratic equation 3u^2 + 5u - 2=0 and i got u = 1/3 and -2 and i have to sub somethin      Log On


   

Question 789099: 1.) Find the solutions of the equation.
I already subuted u for x^(2/3) then i got a quadratic equation 3u^2 + 5u - 2=0 and i got u = 1/3 and -2 and i have to sub something back but I do not know what to do now after i got those two answers for u?
3x^(4/3) + 5x^(2/3) - 2=0
Can someone please help me on this problem and go step by step with this equtaion for me? THANK YOU!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You let u+=+x%5E%282%2F3%29%5E%22%22


So because the first solution for 'u' is u+=+1%2F3, this means...

u+=+1%2F3

x%5E%282%2F3%29%5E%22%22+=+1%2F3

%28x%5E%282%2F3%29%5E%22%22%29%5E3+=+%281%2F3%29%5E3

x%5E2+=+1%2F27

x+=+%22%22%2B-sqrt%281%2F27%29

x+=+sqrt%281%2F27%29 or x+=+-sqrt%281%2F27%29

x+=+sqrt%281%29%2Fsqrt%2827%29 or x+=+-sqrt%281%29%2Fsqrt%2827%29

x+=+1%2Fsqrt%2827%29 or x+=+-1%2Fsqrt%2827%29

x+=+1%2Fsqrt%289%2A3%29 or x+=+-1%2Fsqrt%289%2A3%29

x+=+1%2F%28sqrt%289%29%2Asqrt%283%29%29 or x+=+-1%2F%28sqrt%289%29%2Asqrt%283%29%29

x+=+1%2F%283%2Asqrt%283%29%29 or x+=+-1%2F%283%2Asqrt%283%29%29

x+=+%281%2Asqrt%283%29%29%2F%283%2Asqrt%283%29%2Asqrt%283%29%29 or x+=+-%281%2Asqrt%283%29%29%2F%283%2Asqrt%283%29%2Asqrt%283%29%29

x+=+%28sqrt%283%29%29%2F%283%2A3%29 or x+=+-%28sqrt%283%29%29%2F%283%2A3%29

x+=+%28sqrt%283%29%29%2F%289%29 or x+=+-%28sqrt%283%29%29%2F%289%29

-------------------------------------------------------

Now if u+=+-2, then...

u+=+-2

x%5E%282%2F3%29%5E%22%22+=+-2

%28x%5E%282%2F3%29%5E%22%22%29%5E3+=+%28-2%29%5E3

x%5E2+=+-8

x+=+%22%22%2B-sqrt%28-8%29

x+=+sqrt%28-8%29 or x+=+-sqrt%28-8%29

x+=+sqrt%28-1%2A4%2A2%29 or x+=+-sqrt%28-1%2A4%2A2%29

x+=+sqrt%28-1%29%2Asqrt%284%29%2Asqrt%282%29 or x+=+-sqrt%28-1%29%2Asqrt%284%29%2Asqrt%282%29

x+=+i%2A2%2Asqrt%282%29 or x+=+-i%2A2%2Asqrt%282%29

x+=+2i%2Asqrt%282%29 or x+=+-2i%2Asqrt%282%29

Since these solutions are complex and not real, we can ignore them.

=======================================================

So the two *possible* real numbered solutions are

x+=+%28sqrt%283%29%29%2F%289%29 or x+=+-%28sqrt%283%29%29%2F%289%29

It turns out that when you plug each back into the original equation, only x+=+%28sqrt%283%29%29%2F%289%29 works while x+=+-%28sqrt%283%29%29%2F%289%29 makes the original equation false.

Therefore, the only solution is x+=+%28sqrt%283%29%29%2F%289%29