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How do you find a number that is the sum of two squares and whose square is also the sum of two squares?

Answer 1

Kennedy Adams

If you take any two numbers, square them and add the squares, then the resulting number will satisfy your criteria.

Choose two numbers #a# and #b#.

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 #(a^2+b^2)^2# is the sum of two squares too.

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Answer 2

Kennedy Adams

The smallest number that satisfies these conditions is 5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.