Posted by **Aria** on Tuesday, June 5, 2012 at 9:34pm.

Two consecutive integers are squared. The sum of these squares of these squares is 545. What are the integers?

- Math -
**MathMate**, Tuesday, June 5, 2012 at 10:06pm
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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