This "extra" answer is called an extraneous root. The graphing calculator is a wonderful back-up checking tool to determine if a root is extraneous. Note the example below: ... The calculator clearly shows that there is only one solution (x = 7), thus showing that x = -3 is an extraneous root.
mathbits.com/mathbits/tisection/Algebra2/radicalequatio... mathbits.com/mathbits/tisection/Algebra2/radicalequations.htm
4. checking for possible extraneous roots since the derived equation may not be equivalent to the original equation. The graphing calculator is a wonderful back-up checking tool to solving such equations.
mathbits.com/mathbits/tisection/Algebra2/rationalequati... mathbits.com/mathbits/tisection/Algebra2/rationalequations.htm
It is possible to raise both sides of an equation to an odd power and to extract the odd degree root from both sides of an equation. It is necessary to remember that: a) raising to an even power can result in acquisition of extraneous roots;
www.bymath.com/studyguide/alg/sec/alg12.html
Why does raising an equation to an even power introduce an extraneous root? ... I looked in a couple algebra books and they said that raising an equation to an even power sometimes gives an extraneous root. That still doesn't explain WHY.
mathforum.org/dr.math/problems/duff.9.9.96.html
My question is when, where and why do we use the principle square root, not both + and -? This often occurs as the extraneous root in the solution of radical equations and in stating the domain and range of functions involving square roots.
mathcentral.uregina.ca/QQ/database/QQ.09.96/varjassy2.h... mathcentral.uregina.ca/QQ/database/QQ.09.96/varjassy2.html
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absolute-value A positive number that has the same magnitude as a given number. ... absolute-value function A positive number that has the same magnitude as a given number: f (x) = |x | ... extraneous root A number obtained when solving an equation, which is not a root of the equation to be solved.
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extraneous roots Number Theory discussion ... I attempted to answer the question myself by reversing the above process and putting 1 in for x at each step to see when the equation becomes "invalid" for the extraneous root. equation A; equation B; Putting 1 in for x in equation A works but B does not.
www.physicsforums.com/showthread.php?t=226349