solve: if x=2017,y=2018 and z=2019, find x^2 +y^2 +z^2 −xy−yz−zx


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Question Number 172009 by Mikenice last updated on 23/Jun/22

$s o l v e :$ $i f x = 2017, y = 2018 a n d z = 2019,$ $f i n d x^{2} + y^{2} + z^{2} - x y - y z - z x$
	Answered by som(math1967) last updated on 23/Jun/22
	$x^2 +y^2 +z^2 −xy−yz−zx =(1/2){(x−y)^2 +(y−z)^2 +(z−x)^2 } =(1/2)×{(−1)^2 +(−1)^2 +2^2 } =3$
	$x^{2} + y^{2} + z^{2} - x y - y z - z x$ $= \frac{1}{2} {{(x - y)}^{2} + {(y - z)}^{2} + {(z - x)}^{2}}$ $= \frac{1}{2} \times {{(- 1)}^{2} + {(- 1)}^{2} + 2^{2}}$ $= 3$
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