Posted by Aria on Tuesday, June 5, 2012 at 9:34pm.
Fast way:
Half of 545 = 272 must fall between two perfect sequres, namely 256 and 289, which means that the integers are 16 and 17.
Standard way:
Let x be one of the integers, then x+1 is the other. So that:
x^2+(x+1)^2=545
2x^2+2x-544=0
x^2+x-272=0
(x+17)(x-16)=0
So x=16 or x=-17.
The consecutive integers are therefore:
16, 17, or
-17, -16
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