Solve Algebraic Equation: x⁴+y⁴+z⁴-xyz(x+y+z)

In summary, an algebraic equation is a mathematical statement that contains variables and operations, and the goal is to find the values of the variables that make the equation true. To solve an algebraic equation, you must isolate the variable by using inverse operations. The degree of an algebraic equation is the highest exponent in the equation. This algebraic equation can have more than one solution. To check if the solutions are correct, you can substitute them back into the equation and solve it, or graph the equation and see if the solutions lie on the graph.
  • #1
anemone
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Factorize $x^4+y^4+z^4-xyz(x+y+z)$.
 
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  • #2
anemone said:
Factorize $x^4+y^4+z^4-xyz(x+y+z)$.

is the question correct (that is I am missing something)

$x^4+y^4+z^4-xyz(x+y+z) = x^4-x^2yz - xyz(y+z) + y^4+z^4$ if we put in descending power of x and $y^4+z^4$ does not factor over real coefficients
 
  • #3
kaliprasad said:
is the question correct (that is I am missing something)

$x^4+y^4+z^4-xyz(x+y+z) = x^4-x^2yz - xyz(y+z) + y^4+z^4$ if we put in descending power of x and $y^4+z^4$ does not factor over real coefficients

Ops...it was my mistake to post an incorrect problem...the problem should read:

Find the sum of square factorization for $x^4+y^4+z^4-xyz(x+y+z)$.

Sorry for causing the confusion, folks!:eek:
 
  • #4
needs closure.
 

FAQ: Solve Algebraic Equation: x⁴+y⁴+z⁴-xyz(x+y+z)

What is an algebraic equation?

An algebraic equation is a mathematical statement that contains one or more variables and a set of operations, such as addition, subtraction, multiplication, and division. The goal is to find the values of the variables that make the equation true.

How do you solve an algebraic equation?

To solve an algebraic equation, you must isolate the variable on one side of the equation by using inverse operations. The goal is to get the variable by itself on one side and all other terms on the other side. Once the variable is isolated, you can substitute the solutions back into the equation to check if it is true.

What is the degree of this algebraic equation?

The degree of an algebraic equation is the highest exponent in the equation. In this equation, the degree is 4, as all the terms have an exponent of 4.

Can this algebraic equation have more than one solution?

Yes, this algebraic equation can have more than one solution. In fact, most algebraic equations have more than one solution, unless they are identities or contradictions. In this case, there are infinite solutions as there are three variables and only one equation.

How can I check if my solutions are correct for this algebraic equation?

You can check your solutions by substituting the values back into the equation and solving it. If the equation is true with the given values, then the solutions are correct. You can also graph the equation and see if the solutions lie on the graph.

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