| 单词 | equation |
| 释义 | equation A requirement that a mathematical expression take some particular value. A quadratic equation, for example, takes the form ax2 + bx + c = 0. A solution is any value of x for which this is true. An equation may have more than one argument: for example, ax2 + bxy + cy2 = 0. A solution to this is any set (x, y) for which this equality is satisfied. With simultaneous equations, two or more equations must be satisfied by the same set of their arguments. There is no guarantee that any given equation or set of equations has any real solution, or if it does have one, that this is unique. In a few very special and simple cases it is easy to see whether there are any real solutions and locate them analytically. For many more complex equations and systems of simultaneous equations, it is not easy to tell whether they have solutions, or how many; locating solutions requires number-crunching procedures normally conducted on a computer. See also: difference equation, differential equation, and simultaneous equations |
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