When raising both sides of an equation to the same power, it is possible to introduce extraneous solutions. That is, the equation p = q, is not generally equivalent to pn = qn. If the power n is odd, the equations will have the same real solutions. However, if n is even the solutions must be checked to assure that they solve the original equation.
For example, solve:
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x - 1 = √ x + 5
x2 - 2x + 1 = x + 5 square both sides
x2 - 3x - 4 = 0 rewrite in standard form, and factor
(x - 4)(x + 1) = 0
Then the possible solution set is {4, -1}. Substitution into the original
equation gives:
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x = 4, 3 = √ 9
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x = -1, -2 ≠ √ 4
We see that, x = 4 is a solution and x = -1 is extraneous.