Fiber of Truth/Examples/x^2 - 2x - 3

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Example of Solution Set

Consider the equation in algebra:

$x^2 - 2 x - 3 = 0$

where the domain of $x$ is implicitly taken to be the set of real numbers $\R$.


Then $3$ is a solution to $x^2 - 2 x - 3 = 0$.


Proof

We have that:

\(\ds 3^2 - 2 \times 3 - 3\) \(=\) \(\ds 9 - 6 - 3\)
\(\ds \) \(=\) \(\ds 0\)

and the result follows by definition of solution.

$\blacksquare$


Sources