mac1140_lecture10_2

# mac1140_lecture10_2 - L10 §2.6 Other Types of Equations...

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Unformatted text preview: L10 §2.6 Other Types of Equations Example. Solve: 1 − 2 x = 3 . Equations with Radicals (Rational Exponents): In order to solve an equation with radicals/rational exponents, simplify the equation, isolate one radical on one side, and raise both sides to the same power as the index of the radical in order to eliminate the radical. You may need to repeat this procedure if the resulting equation still contains a radical. Example. Solve: 6 x + 13 = 2 x + 1. Be careful! If you raise both sides of an equation to an even power, the new equation may not be necessary equivalent to the original one and have more real solutions. Example: The equation x = 6 has solution set {6}. Squaring both sides gives the equation x 2 = 36 , which has solutions x = ±6 and, therefore, is not equivalent to the original equation. x = −6 does not solve the original equation and must be rejected. Important: When raising to an even power, always check each proposed solution in the original equation. 78 79 Example. Solve: 4 9 − x = −18 . Example. Solve: 5a − 2a − 1 = 2 . Remember: If n is even, n a is the principle nth root of a, and its value cannot be negative. 1 4 Example. Solve: (13 x − 36 ) = x . 2 80 81 2 3 1 3 Example. Solve: ( x − 2) − 6( x − 2) − 7 = 0 . 82 Example. Solve by factoring: 1 4 x( x 2 − 3 x) 3 + 2( x 2 − 3 x) 3 = 0 83 ...
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mac1140_lecture10_2 - L10 §2.6 Other Types of Equations...

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