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))

Harrison Mills

Harrison Mills

Answered question

2022-09-20

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.

Answer & Explanation

wayiswa8i

wayiswa8i

Beginner2022-09-21Added 6 answers

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

Colten Andrade

Beginner2022-09-22Added 3 answers

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

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