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:
“You can’t have operations without screams. Pain and the knife—they’re inseparable.”
—Jean Scott Rogers. Robert Day. Mr. Blount (Frank Pettingell)
“Plot, rules, nor even poetry, are not half so great beauties in tragedy or comedy as a just imitation of nature, of character, of the passions and their operations in diversified situations.”
—Horace Walpole (1717–1797)