Fraction solving related If a + b + c = 0, then evaluate a 4 + b 4 + c 4 a 2 b 2 + c 2 ( a 2 + b 2 ) I tried solving but could make to mentionworthy progress.

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Fraction solving related If  a  +  b  +  c  =  0, then evaluate                    a        4            +              b        4            +              c        4                            a        2                    b        2            +              c        2            (              a        2            +              b        2            )      I tried solving but could make to mentionworthy progress.

wayiswa8i · Accepted Answer

a  +  b  =  −  c  ,      a    2    +      b    2    =      c    2    −  2  a  b                    a        4            +              b        4            +              c        4                            a        2                    b        2            +              c        2            (              a        2            +              b        2            )          ⟺              (              a        2            +              b        2                    )        2            −      2              a        2                    b        2            +              c        4                            a        2                    b        2            +              c        2            (              a        2            +              b        2            )          ⟺              (              c        2            −      2      a      b              )        2            −      2              a        2                    b        2            +              c        4                            a        2                    b        2            +              c        2            (              c        2            −      2      a      b      )          ⟺                      c        4            −      4      a      b              c        2            +      4              a        2                    b        2            −      2              a        2                    b        2            +              c        4                            c        4            −      2      a      b              c        2            +              a        2                    b        2                ⟺              2              c        4            −      4      a      b              c        2            +      2              a        2                    b        2                            c        4            −      2      a      b              c        2            +              a        2                    b        2              =  2

Colten Andrade · Accepted Answer

this is                    a        4            +              b        4            +      (      −      a      −      b              )        4                            a        2                    b        2            +      (      −      a      −      b              )        2            (              a        2            +              b        2            )        =  2after simplifying

Fraction solving related If a+b+c=0 , then evaluate (a^4 + b^4 + c^4)/(a^2b^2 + c^2(a^2 + b^2))

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