NRICH: Perfectly Square

The sums of the squares of three related numbers is also a perfect square – can you explain why?

We are first given that:

x1=++
x2=++12²
x3=++20²

Then show that xₙ is always a perfect square.

Age 14 to 16


Math Topics
Algebra & Pre-Algebra, Quadratic Equations
High School, Educator
9th Grade, 10th Grade, 11th Grade

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NRICH (University of Cambridge)

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Challenge

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