The number of triples satisfying x^4+y^4+z^4+1=4xyz
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★ THEORY OF NUMBERS ★
GIVEN EXPRESSION :
x⁴ + y⁴ + z⁴ + 1 = 4xyz
By mathematical generality , in L.H.S.
only two such satisfactory possible integers are available ,
1 and -1
both constituting even raised exponents and offers uniform symmetry equivalent to the result -
1 + 1 + 1 + 1 = 4 (1)(1)(1)
-1 is rejected for violation case in R.H.S.
HENCE , ONLY 1 TRIPLET IS POSSIBLE
( 1, 1 ,1 )
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GIVEN EXPRESSION :
x⁴ + y⁴ + z⁴ + 1 = 4xyz
By mathematical generality , in L.H.S.
only two such satisfactory possible integers are available ,
1 and -1
both constituting even raised exponents and offers uniform symmetry equivalent to the result -
1 + 1 + 1 + 1 = 4 (1)(1)(1)
-1 is rejected for violation case in R.H.S.
HENCE , ONLY 1 TRIPLET IS POSSIBLE
( 1, 1 ,1 )
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
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