Question 1040358
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If x = 2015, y = 2014 and z = 2013, then the value of
x² + y² +z² – xy – yz – zx is
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<pre>
   {{{x^2 + y^2 + z^2 - xy - yz - zx}}} = 

= {{{(x^2 - xy) + (y^2-yz) + (z^2-zx)}}} = 

= {{{x*(x-y) + y*(y-z) + z*(z-x)}}} = 

= 2015*1 + 2014*1 + 2013*(-2) =  2015 + 2014 - 2*2013 = (2015-2013) + (2014-2013) = 3.
</pre>

The right and more effective question would be "calculate without a calculator".