## anonymous one year ago what are the values of x in this equation? x^(2/5)+x^(1/5)+1=3 answers: 32,-1 32,1 -32,1 -32,-1

1. Theloshua

ummmm okay, so the first thing your gonna do is subtract one from both sides

2. anonymous

Subtract 3 from both sides, because then one side will be 0 and you can factor or use the quadratic equation

3. Theloshua

$x ^{\left(\begin{matrix}2 \5\ ?\end{matrix}\right)} + x ^{\left(\begin{matrix}1 \5 \ ?\end{matrix}\right)}=3$

4. Theloshua

is that the equation?

5. anonymous

the equation is x^(2/5)+x^(1/5)+1=3

6. anonymous

how do i subtract 3 from the left side? do i plug in the numbers first?

7. anonymous

x^(2/5) + x^(1/5) + 1 = 3 x^(2/5) + x^(1/5) - 2 = 0

8. Theloshua

9. anonymous

you can do a change of variables. Let u = x^(1/5), then the equation becomes u² + u - 2 = 0 Solve the quadratic equation for u Then go back and solve for x

10. anonymous

so its 32 and 1 that equals 3 right?

11. anonymous

32^2/5+1^1/5-2=0

12. anonymous

no it doesn't work that way. The solutions have to work individually. You can't mix them. Factor the quadratic equation I put above to get solutions for u

13. anonymous

hello

14. anonymous

u^2+u=2 u(u+1)=2 u=1

15. anonymous

how to i solve for x? x^(1/5)=1? is that how i do it?

16. anonymous

if that is the value of u, then yes, there should be 2 values for u though

17. anonymous

how do I get two values for u then?

18. anonymous
19. anonymous

20. anonymous

they aren't using the same kind of numbers i am. what am i doing wrong?

21. anonymous

Refer to the attachment from Mathematica 9.

22. anonymous

@robtobey how does that help me?

23. anonymous

24. anonymous

you didn't factor that right. the video @billj5 posted shows you how to factor. @robtobey gave you the answer

25. anonymous

where is the answer in it?

26. anonymous

none of your options are going to work because 1 is the only solution to this equation.

27. anonymous

that's what i thought but it doesn't give me an option for just 1.

28. anonymous

ok. let's see if we can find another Factor this u² + u - 2 = 0 What 2 numbers multiply to -2 and add to 1?

29. anonymous

1?

30. anonymous

Quadratic equations have 2 solutions, so we need TWO numbers. Look at the factors of -2 and then figure out which pair adds to 1.

31. anonymous

?

32. anonymous

i still don't understand any of this. :(

33. anonymous

i figured it out!!

34. anonymous

ok. What did you get?

35. anonymous

-32,1

36. anonymous

yeah that's right :)