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If $x = \sqrt{2006}$ and $y = \sqrt{2007}$, what is the simplified value of $(x + y)^2 + (x - y)^2$?

 Jan 5, 2021
 #1
avatar+285 
+3

Answer: 

(x+y)2+(xy)2

(2006+2007)+(20062007)

(3223+2006)2+(20062007)2

(3223+2006)2+(20063223)2

4013+6447338+(20063223)2

4013+6447338+40136447338

8026

 Jan 5, 2021
 #2
avatar+44 
+1

hihihi's solution is good, but this one may help you solve the problem quicker and easier

 

 

(x+y)2 = x2+2xy+y2

(x-y)2=x2-2xy+y2

As such, when you add them together, you get 2x2+2y2

When you plug in x and y, this equals to 2(2006)+2(2007)=4012+4014=8026

 Jan 5, 2021

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