- #1
rabihtawil
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Homework Statement
how to solve this:
4x3 + 4y =0
4y3 + 4x =0
the solution is x = 0,1,-1
y = 0,-1,1
how did they bring such result
Solving 4x3 + 4y =0 and 4y3 + 4x =0: Explained!
- Thread starter rabihtawil
- Start date
In summary, the solution to the given equations is x = 0,1,-1 and y = 0,-1,1. To find these solutions, one can solve for y in the first equation and then plug it into the second equation. After fixing an algebra mistake, the polynomial can be factored to find the roots.
how to solve this:
4x3 + 4y =0
4y3 + 4x =0
the solution is x = 0,1,-1
y = 0,-1,1
how did they bring such result
- #2
Altabeh
- 660
- 0
rabihtawil said:Homework Statement
how to solve this:
4x3 + 4y =0
4y3 + 4x =0
the solution is x = 0,1,-1
y = 0,-1,1
how did they bring such result
Find y from the first equation and then plug it into the second one so you're done!
AB
- #3
rabihtawil
- 10
- 0
Altabeh said:
4x3 + 4y =0
x3 + y=0
y=x3
NOW... plugging in
4y3 + 4x =0
y3 + x=0
(x3)3 + x = 0
now what?? how do i continue from here :S
- #4
vela
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First, fix your algebra mistake. You dropped a sign. Once you fix that, you'll find you can factor the polynomial and solve for its roots.
- #5
rabihtawil
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- 0
vela said:
4x3 + 4y =0
x3 + y=0
y=-x3
NOW... plugging in
4y3 + 4x =0
y3 + x=0
(-x3)3 + x = 0
vela said:
Please i am stuck show me how, i know it should be factored by x but how?
Last edited:
- #6
vela
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First, simplify (-x3)3. What do you get?
- #7
rabihtawil
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vela said:
-x9 + x = 0
now what?
- #8
rabihtawil
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rabihtawil said:
-x9 + x = 0
x(-x8 + 1) = 0
x = 0 or x= 1 right?
- #9
vela
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You can flip the sign of the whole equation to make it a little simpler to work with:
x9-x=0
Now you have a common factor of x in both terms, so factor it out.
OK, you posted while I was writing. :) So you have
x(x8-1) = 0
So this means x=0 or x8-1=0, right? So you have one of the roots so far.
Note that x8-1=(x4)2-12 is a difference of squares, so what does it factor into?
x9-x=0
Now you have a common factor of x in both terms, so factor it out.
OK, you posted while I was writing. :) So you have
x(x8-1) = 0
So this means x=0 or x8-1=0, right? So you have one of the roots so far.
Note that x8-1=(x4)2-12 is a difference of squares, so what does it factor into?
- #10
rabihtawil
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Thank you so much, very appreciated!
FAQ: Solving 4x3 + 4y =0 and 4y3 + 4x =0: Explained!
What is the equation being solved in "Solving 4x3 + 4y =0 and 4y3 + 4x =0: Explained!"?
The equation being solved is a system of two equations with three variables (x, y, and z). The equations are 4x3 + 4y = 0 and 4y3 + 4x = 0.
Why are there two equations in the system?
A system of equations is used when there are multiple unknown variables and we need to find values that satisfy all the equations. In this case, the system has two equations because there are two unknown variables (x and y).
What is the purpose of solving this system of equations?
The purpose of solving a system of equations is to find values for the variables that satisfy both equations. This allows us to find the intersection point(s) of the two equations, which can be used in various applications such as optimization problems or finding solutions to real-world problems.
What is the process for solving this system of equations?
The process for solving a system of equations involves using algebraic manipulation and substitution to eliminate one variable and solve for the other. In this case, we can use the substitution method by solving one equation for one variable and plugging it into the other equation.
Can this system of equations have multiple solutions?
Yes, the system of equations can have multiple solutions, depending on the values of the variables. In this case, there can be multiple intersection points between the two equations, leading to different solutions for x and y.