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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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 Fall '11
 gregory
 Radicals, Equations, Exponents

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