jmc

Question

The positive difference between two consecutive even perfect squares is 268. Compute the larger of the two squares.

Accepted Answer

Let the larger square be x^2, and the smaller one be (x-2)^2. Their difference is x^2-(x-2)^2=(x-(x-2))(x+(x-2))=2(2x-2)=4(x-1)Thus, 4(x-1)=268 x-1=67. So x=68 and the answer is 68^2=4624.