If x = 2015, y = 2014 and z = 2013, then value of x2 +

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If x = 2015, y = 2014 and z = 2013, then value of x² + y² + z² – xy – yz – zx is

x – y = 2015 – 2014 = 1
y – z = 2014 – 2013 = 1
z – x = 2013 – 2015 = –2

∴ x² + y² + z² – xy – yz – zx =	1	[ 2x² + 2y² + 2z² – 2xy – 2yz – 2zx ]
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⇒ x² + y² + z² – xy – yz – zx =	1	[ x² + y² – 2xy + y² + z² – 2yz + z² + x² – 2zx ]
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⇒ 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 ]
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⇒ x² + y² + z² – xy – yz – zx =	1	[ 1 + 1 + 4 ]
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⇒ x² + y² + z² – xy – yz – zx =	1	× 6 = 3
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