MediumHow to solve √(5-x) = 5 — x² using equivalence - YouPhysics - Medium
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How to solve √(5-x) = 5 — x² using equivalence

Oct 18, 2026

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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

Press enter or click to view image in full size

Both expressions obtained are equivalent, up to a rotation of the coordinate systems about the bisector, where x = u, or u = x.

Therefore:

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YouPhysics

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