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

Algebra ->  Equations -> SOLUTION: If x = 2015, y = 2014 and z = 2013, then the value of x² + y² +z² – xy – yz – zx is      Log On


   

Question 1040358: If x = 2015, y = 2014 and z = 2013, then the value of
x² + y² +z² – xy – yz – zx is
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
If x = 2015, y = 2014 and z = 2013, then the value of
x² + y² +z² – xy – yz – zx is
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

   x%5E2+%2B+y%5E2+%2B+z%5E2+-+xy+-+yz+-+zx = 

= %28x%5E2+-+xy%29+%2B+%28y%5E2-yz%29+%2B+%28z%5E2-zx%29 = 

= x%2A%28x-y%29+%2B+y%2A%28y-z%29+%2B+z%2A%28z-x%29 = 

= 2015*1 + 2014*1 + 2013*(-2) =  2015 + 2014 - 2*2013 = (2015-2013) + (2014-2013) = 3.

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