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Extraneous solutions turn up in a few different p;aces in algebra. One reason they turn up in logarithmic equations is that you can only have a log of a positive number, but when you solve the equation, one of the answers is negative.
Did you ever do a word problem about a rectangle and have to solve a quadratic equation? You probably got 2 answers, and had to reject one of them because the length of a rectangle can't be negative. Same idea: the algebra doesn't understand what the problem is about, it just churns out answers!
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What does extraneous mean What must you do to determine whether a solution is an extraneous solution?
Extraneous means extra and unnecessary. Extraneous solutions are values that can arise from the process of solving the equation but do not in fact satisfy the initial equation. These solutions occur most often when not all parts of the process of solving are not completely reversible - for example, if both sides of the equation are squared at some point.
What is a solution of an eqaution derived from an original equation that is not a solution of the original equation?
Extraneous solution
What must you do to determine weather a soluion is an exraneous solution?
If the solution, makes the denominator equal to zero, makes the expression of a logarithm or under a square root, a negative one. If there are more than one denominator, check all the solutions. Usually, we determine the extraneous solutions before we solve the equation.
Which pairs are solutions to the equation?
That depends on the equation.
What do you call the solution of a equation derived from an original equation that is not a solution of the original equation?
That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.
