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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.
Depending on the context, solving an equation may consist to find either any solution (finding a single solution is enough), all solutions, or a solution that satisfies further properties, such as belonging to a given interval. When the task is to find the solution that is the best under some criterion, this is an optimization problem. Solving ...
If some function is applied to both sides of an equation, the resulting equation has the solutions of the initial equation among its solutions, but may have further solutions called extraneous solutions. For example, the equation = has the solution =
5 Extraneous solutions in applied problems. 1 comment. 6 Example with the imaginary unit, i. 1 comment. Toggle the table of contents. Talk: Extraneous and missing ...
This procedure gives extraneous solutions, but when the correct ones have been found by numerical means, the roots of the quintic can be written in terms of square roots, cube roots, and the Bring radical, which is therefore an algebraic solution in terms of algebraic functions (defined broadly to include Bring radicals) of a single variable ...
Shoppers generally are reducing extraneous purchases, and if they do need cosmetics, many are switching down to more affordable alternatives. E.l.f. is reporting high growth, and it's also profitable.
You can still find accounts paying out more than 10 times the 0.42% national average — up to 5.05% APY with none of the fees, high minimums or stiff penalties that can eat into the interest you ...
Summary: Lacey Chabert stars as Kathy, a grieving widow who accidentally brings a snowman to life with a magic scarf.When she takes the responsibility of looking after the living snowman (Dustin ...