mac1147_lecture8_1_c

# mac1147_lecture8_1_c - L8 Other Types of Equations...

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71 L8 Other Types of Equations Equations with Radical and Rational Exponents When solving an equation linear in form with radicals or rational exponents, simplify the equation, isolate the most complicated radical on one side, and then raise both sides to the power equal to the index of the radical in order to eliminate the last. You may need to repeat this procedure if the resulting equation still contains a radical. Note : We solve radical equations over the real numbers. Caution! If you raise both sides of an equation to an even power , the new equation may have more real solutions than the original one. Example : Equation 6 x = has solution set: {6}. Raising both sides to the power 2, gives the equation 2 36 x = which has solution set 6 x = ± . Thus, 6 x =− is an extraneous solution of the original equation and must be rejected. Important ! When raising to an even power, always check each proposed solution in the original equation.

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72 Example : Solve 21 5 4 0 x x −= . Example : Solve 4 91 8 x =− . Note : If n is an even number , n a is never negative

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## This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_lecture8_1_c - L8 Other Types of Equations...

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