How do you find a number that is the sum of two squares and whose square is also the sum of two squares?
1 Answer
Jul 31, 2017
If you take any two numbers, square them and add the squares, then the resulting number will satisfy your criteria.
Explanation:
Choose two numbers
Then:
#(a^2-b^2)^2 + (2ab)^2 = (a^4-2a^2b^2+b^4) + 4a^2b^2#
#color(white)((a^2-b^2)^2 + (2ab)^2) = a^4+2a^2b^2+b^4#
#color(white)((a^2-b^2)^2 + (2ab)^2) = (a^2+b^2)^2#
That is
