If x = 997, y = 998 and z = 999, then the value of x2 +

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If x = 997, y = 998 and z = 999, then the value of x² + y² + z² – xy – yz – zx is

x = 997 , y = 998 , z = 999
∴ x – y = 997 – 998 = –1
y – z = 998 – 999 = –1
z – x = 999 – 997 = 2

∴ x² + y² + z² – xy – yz – zx =	1	[ 2x² + 2y² + 2z² – 2xy – 2yz – 2zx ]
	2

⇒ x² + y² + z² – xy – yz – zx =	1	[ x² + y² – 2xy + y² + z² – 2yz + z² + x² – 2zx ]
	2

⇒ x² + y² + z² – xy – yz – zx =	1	[ (x - y)² + (y - z)² + (z - x)² ]
	2

⇒ x² + y² + z² – xy – yz – zx =	1	[ (-1)² + (-1)² + (2)² ]
	2

⇒ x² + y² + z² – xy – yz – zx =	1	[ 1 + 1 + 4 ]
	2

⇒ x² + y² + z² – xy – yz – zx =	1	× 6 = 3
	2