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find x,y,z real triples satisfying the given condition x^4+y^4+z^4-4xyz=-1

find x,y,z real triples satisfying the given condition


x^4+y^4+z^4-4xyz=-1

Grade:12

1 Answers

Amit Jain
askIITians Faculty 32 Points
7 years ago
The whole equation can be re-arranged to (x2-y2)2+(z2-1)2+2(xy-z)2=0
All three squares must be zero. So the triplets can be found out correspondingly as (1,1,1), (-1,1,-1),(1,-1,-1).

Amit Jain
IIT Delhi
AskIITians Faculty

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