Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

is that the equation?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

oh wait, your right :D do your thing XD

Answer 9

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

Answer 10

so its 32 and 1 that equals 3 right?

Answer 11

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

Answer 12

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

Answer 13

hello

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

how do I get two values for u then?

Answer 18

like this https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_factoring/v/example-1-solving-a-quadratic-equation-by-factoring

Answer 19

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

Answer 20

Refer to the attachment from Mathematica 9.

Answer 21

@robtobey how does that help me?

Answer 22

It provides the right answer.

Answer 23

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

Answer 24

where is the answer in it?

Answer 25

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

Answer 26

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

Answer 27

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?

Answer 28

1?

Answer 29

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.

Answer 30

?

Answer 31

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

Answer 32

i figured it out!!

Answer 33

ok. What did you get?

Answer 34

-32,1

Answer 35

yeah that's right :)