An algebra problem by Aman Goenka

Algebra Level 4

( X 2 − Y Z ) 3 + ( Y 2 − Z X ) 3 + ( Z 2 − X Y ) 3 − 3 ( X 2 − Y Z ) ( Y 2 − Z X ) ( Z 2 − X Y ) ( X^{2} -YZ)^{3} + ( Y^{2} -ZX) ^{3} + (Z^{2}-XY)^{3} - 3( X^{2} - YZ) (Y^{2} -ZX)( Z^{2} - XY)

Is this a perfect square YES or NO??? If YES then whats its square root.... And if NO then whats its square root?????

No, its not a perfect square.... and its square root is \sqrt{31} Yes, its a perfect square.. and its square root is 2. Yes, its a perfect.. and its square root is 4. No, its not a perfect square.. and its square root is \sqrt{3}.

Aman Goenka by Aman Goenka , 22, India

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