How to solve √(5-x) = 5 — x² using equivalence
Solving this equation using the traditional method requires many steps; however, it can be solved by preliminary inspection, applying the principle of mathematical equivalence.
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By making a change to the second term:
where u is a dependent variable, and then solving for x:
On the other hand, if we write it differently, by setting x as the dependent variable:
e resolvendo para u, por analogia teremos:
Illustrating graphically in the figure below the trivial aspect of equivalence
Both expressions obtained are equivalent, up to a rotation of the coordinate systems about the bisector, where x = u, or u = x.
Therefore:






