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

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The discussion revolves around the factorization of the expression x⁴+y⁴+z⁴-xyz(x+y+z). Initially, there was confusion regarding the problem's formulation, leading to a clarification that the correct task is to find the sum of square factorization for the expression. Participants express understanding and seek the proper approach to solve the revised problem. The conversation emphasizes the importance of accurately stating mathematical problems to avoid confusion. The thread concludes with a request for closure on the corrected problem.
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Factorize $x^4+y^4+z^4-xyz(x+y+z)$.
 
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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
 
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!:o
 
needs closure.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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