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The function f(x) has the property that f (x+y) = f(x)+f(y)+2xy, for all positive integers x and y. If f(1) = 4, then what is the value of f(8)?

 Oct 16, 2018
 #1
avatar+5 
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So, this is a really fun pattern problem. Now, since you already know f(1), it will be advantageous to write f(1+y) as f(n), and say that for f(8), y=7. Then start checking to see if there's a pattern which you can gneralize in terms of n, while n=y+1. Remember that f(x) is a known variable, and that y equals n-1. A hint: remember the factorials.

 Oct 16, 2018
 #2
avatar+316 
+1

I guess f(2)= f(1) + f(1) + 2(1)(1) = 4 + 4 + 2 =10 ,f(4) = f(2) + f(2) + 2(2)(2) = 10 +10 + 8 = 28 

f(8) = f(4) + f(4) +2(4)(4) = 28 + 28 + 32 = 88 

So i think f(8) = 88 

Hope it helps!

 Oct 16, 2018

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