Common silly mistake
Algebra
Level
5
A common mistake made by students is to claim that
\[ \sqrt{a^2+b^2} = \sqrt{a^2} + \sqrt{b^2} .\]
How many ordered triples of integers \( (a, b, c) \) are there, such that each of \(a,b,c\) are integers from 0 to 9 inclusive, and
\[ \sqrt{ a^2 + b^2} - \sqrt{a^2 + c^2} = \sqrt{b^2} - \sqrt{c^2} ? \]
by
Calvin Lin