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

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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

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ummmm okay, so the first thing your gonna do is subtract one from both sides
Subtract 3 from both sides, because then one side will be 0 and you can factor or use the quadratic equation
\[x ^{\left(\begin{matrix}2 \5\ ?\end{matrix}\right)} + x ^{\left(\begin{matrix}1 \5 \ ?\end{matrix}\right)}=3\]

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Other answers:

is that the equation?
the equation is x^(2/5)+x^(1/5)+1=3
how do i subtract 3 from the left side? do i plug in the numbers first?
x^(2/5) + x^(1/5) + 1 = 3 x^(2/5) + x^(1/5) - 2 = 0
oh wait, your right :D do your thing XD
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
so its 32 and 1 that equals 3 right?
32^2/5+1^1/5-2=0
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
hello
u^2+u=2 u(u+1)=2 u=1
how to i solve for x? x^(1/5)=1? is that how i do it?
if that is the value of u, then yes, there should be 2 values for u though
how do I get two values for u then?
like this https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_factoring/v/example-1-solving-a-quadratic-equation-by-factoring
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they aren't using the same kind of numbers i am. what am i doing wrong?
Refer to the attachment from Mathematica 9.
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@robtobey how does that help me?
It provides the right answer.
you didn't factor that right. the video @billj5 posted shows you how to factor. @robtobey gave you the answer
where is the answer in it?
none of your options are going to work because 1 is the only solution to this equation.
that's what i thought but it doesn't give me an option for just 1.
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?
1?
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.
?
i still don't understand any of this. :(
i figured it out!!
ok. What did you get?
-32,1
yeah that's right :)

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