Question

Solve systems numerically.
x^3=4x^3-2
I am stuck and have no idea what to do next. I know I have to eventually find a point (x,y) where they intersect.

Answer 1

move x in one side
so x^3-4x^3=-3

Answer 2

just add now

Answer 3

Okay, so I add 3 to what though? x^3-4x^3?

Answer 4

-3x^3=-2

Answer 5

divid by -3 both side

Answer 6

*sides

Answer 7

Okay I will, one minute

Answer 8

I got x^3=2/3. Is that correct?

Answer 9

yes..... now take cubic squr.

Answer 10

cubic square?

Answer 11

sorry cubic root

Answer 12

\[x=\sqrt[3]{\frac{ 2 }{ 3 }}\]

Answer 13

Once you have x, don’t forget to find y (or f(x) ), since you should be finding a point (x,y) where these intersect. This is what my teacher said, if that helps.

Answer 14

\[x ^{3}=\frac{ 2 }{ 3 }\]
taking the cubic root for both sides
\[\sqrt[3]{x ^{3}}=\sqrt[3]{\frac{ 2 }{ 3 }}\]
\[x=\sqrt[3]{\frac{ 2 }{ 3 }}\]

Answer 15

but where is y in the function!

Answer 16

There is none so I think she meant to just find f(x)

Answer 17

The original problem was f(x)=x^3 and g(x)=4x^3-2. And it just said to solve the systems numerically. And there is supposed to be a point where (x,y) they intersect.

Answer 18

okay then you don't need to solve for x since x is cubed. you just let x^3=2/3. use this value in f(x)

Answer 19

Okay, so how exactly do I start solving for f(x)?

Answer 20

f(x)=x^3 so if x=0, f(x)=0 x=2, f(x)=8

Answer 21

Do I need to solve any further or are those just the (x,y) points?

Answer 22

but using the value that you go 2/3 is where they should intersect

Answer 23

no
\[x=\sqrt[3]{\frac{ 2 }{ 3 }}\]
f(x)=2/3
g(x)=4(2/3)-2=8/3-2=(8-6)/3=2/3

Answer 24

Okay, so those are the final answers then?

Answer 25

yes

Answer 26

Okay, thank you so much for taking the time to help me. I was so confused. You're a life saver.