Other Operations
Multiplication and division are not the only operations that can modify the solution set. For example, take the problem:
If we take the positive square root of both sides, we get:
We're not taking the square root of any negative values here, since both x2 and 4 are necessarily positive. But we've lost the solution x = −2. The reason is that x is actually not in general the positive square root of x2. If x is negative, the positive square root of x2 is -x. If the step is taken correctly, it leads instead to the equation:
This equation has the same two solutions as the original one: x = 2, and x = −2.
Read more about this topic: Extraneous And Missing Solutions
Famous quotes containing the word operations:
“It may seem strange that any road through such a wilderness should be passable, even in winter, when the snow is three or four feet deep, but at that season, wherever lumbering operations are actively carried on, teams are continually passing on the single track, and it becomes as smooth almost as a railway.”
—Henry David Thoreau (1817–1862)
“A sociosphere of contact, control, persuasion and dissuasion, of exhibitions of inhibitions in massive or homeopathic doses...: this is obscenity. All structures turned inside out and exhibited, all operations rendered visible. In America this goes all the way from the bewildering network of aerial telephone and electric wires ... to the concrete multiplication of all the bodily functions in the home, the litany of ingredients on the tiniest can of food, the exhibition of income or IQ.”
—Jean Baudrillard (b. 1929)