Common silly mistake

Algebra Level 5

A common mistake made by students is to claim that

a2+b2=a2+b2. \sqrt{a^2+b^2} = \sqrt{a^2} + \sqrt{b^2} .

How many ordered triples of integers (a,b,c) (a, b, c) are there, such that each of a,b,ca,b,c are integers from 0 to 9 inclusive, and

a2+b2a2+c2=b2c2? \sqrt{ a^2 + b^2} - \sqrt{a^2 + c^2} = \sqrt{b^2} - \sqrt{c^2} ?

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