Question

How many pairs of integers (x,y) are there such that 2x2−2xy+y2=225?

Answer 1

is it 2x^2?

Answer 2

yup, its 2x^2-2xy+y^2=225.

Answer 3

\[ 2x^2 -2xy + y^2 = x^2 + (x-y)^2 = 225 = 15^2 \\
\]
this is same as \( a^2 + b^2 = 15^2 \)

Answer 4

you can use this formula to compare and find the integers
http://mathworld.wolfram.com/images/equations/PythagoreanTriple/NumberedEquation5.gif from here http://mathworld.wolfram.com/PythagoreanTriple.html