Solution of Equation/Examples/x^2 - 2x - 3

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

• 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations ... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $3$: The Differential Equation