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Therefore, the solution = is extraneous and not valid, and the original equation has no solution. For this specific example, it could be recognized that (for the value x = − 2 {\displaystyle x=-2} ), the operation of multiplying by ( x − 2 ) ( x + 2 ) {\displaystyle (x-2)(x+2)} would be a multiplication by zero.
When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values (one for each unknown) such that, when substituted for the unknowns, the equation becomes an equality.
where x = 7 is the solution to the problem, and x = -4 is an extraneous solution because it is not pertinent to the problem. Tparameter 17:46, 19 January 2008 (UTC) No, this is not a sutiable example of an extraneous solution. Since x = -4 can satisfly the equation x 2 - 3x + 5 = 0, only does not satisfly the domain that sets manually.
The first use of an equals sign, equivalent to 14x + 15 = 71 in modern notation. From The Whetstone of Witte by Robert Recorde of Wales (1557). [1]In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =.
A solution that has no extension is called a maximal solution. A solution defined on all of R {\displaystyle \mathbb {R} } is called a global solution . A general solution of an n {\displaystyle n} th-order equation is a solution containing n {\displaystyle n} arbitrary independent constants of integration .
An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula . For example, a solution of table salt , also known as sodium chloride (NaCl), in water would be represented as Na + (aq) + Cl − (aq) .
So, don't scroll any further if you don't want to see the solutions! The answers to today's Connections Sports Edition #141 are coming up next. Related: 15 Fun Games Like Connections to Play Every ...
Let be a Banach space, let ′ be the dual space of , let : ′ be a linear map, and let ′.A vector is a solution of the equation = if and only if for all , () = ().A particular choice of is called a test vector (in general) or a test function (if is a function space).