Find the larger integer

Algebra Level pending

I am thinking of two consecutive positive odd integers. The square of the larger integer is 64 greater than the square of the smaller integer. Find the larger integer.


The answer is 17.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Let x x be the smaller integer, then the larger integer is x + 2 x+2 . From the data given, we have

( x + 2 ) 2 = x 2 + 64 (x+2)^2=x^2+64

x 2 + 4 x + 4 = x 2 + 64 x^2+4x+4=x^2+64

4 x = 60 4x=60

x = 15 x=15

Finally, the desired answer is x + 2 = 15 + 2 = 17 x+2=15+2=\boxed{17}

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