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

  • Thread starter Thread starter anemone
  • Start date Start date
  • Tags Tags
    Algebra Challenge
AI Thread Summary
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.
anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
Factorize $x^4+y^4+z^4-xyz(x+y+z)$.
 
Mathematics news on Phys.org
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.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top