Reciprocal Equation/Examples/Arbitrary Example 1

Example of Reciprocal Equation

The equation:

$x^2 + 1 = 0$

is an example of a reciprocal equation.

Proof

Replacing $x$ with $\dfrac 1 x$ gives:

$\dfrac 1 {x^2} + 1 = 0$

which, on multiplying through by $x^2$, gives:

$1 + x^2 = 0$

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): reciprocal equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): reciprocal equation