If x = \sqrt{2006} and y = \sqrt{2007}, what is the simplified value of (x + y)^2 + (x - y)^2?
+26367 If
\(x = \sqrt{2006}\) and \(y = \sqrt{2007}\),
what is the simplified value of
\((x + y)^2 + (x - y)^2\)?
\(\begin{array}{|rcll|} \hline (x + y)^2 + (x - y)^2 &=& x^2+2xy+y^2+x^2-2xy+y^2 \\ &=& x^2+y^2+x^2+y^2 \\ &=& 2x^2+2y^2 \\ &=& 2(x^2+y^2) \quad | \quad x^2=2006,~y^2=2007 \\ &=& 2(2006+2007) \\ &=& 2*2013 \\ \mathbf{ (x + y)^2 + (x - y)^2 } &=& \mathbf{4026} \\ \hline \end{array}\)
