Exact solution意思

"Exact solution" is a term used in mathematics, particularly in the context of solving equations or problems. It refers to a solution that is precise and definitive, without any elements of approximation or estimation. In other words, an exact solution is the true value that satisfies the given conditions or equations exactly, without any rounding, truncation, or error.

For example, consider the equation x^2 = 9. The exact solutions to this equation are x = 3 and x = -3, because these are the precise values that make the equation true when squared. If someone were to give you an answer like "x is about 3" or "x is approximately -3," those would not be considered exact solutions because they are not precise enough.

The concept of an exact solution is especially important in fields like physics, engineering, and chemistry, where precise calculations are necessary for accurate results. In contrast, in some contexts where the level of precision is not critical or where the exact solution is difficult to obtain, an approximate solution may be sufficient.