Roots and Rational Exponents
Recall that can be defined as follows:
1. If is odd, then is the number such that .
2. If is even and , then is the number such that . (Notice that is undefined if is even and .
We can define rational exponents in the following manner:
If is a fraction reduced to lowest terms, then
assuming that if is even.
Ex 1 Solve the equation .
Sol Squaring both sides gives , and then subtracting from both sides gives . Then factoring gives , so or . However, does not check in the original equation, so is the only solution.
Ex 2 Solve the equation .
Sol a Adding 6 to both sides gives , and then factoring gives , so either or and therefore or .
Sol b Adding to both sides gives , and then squaring both sides gives ; so or .
Pr 1 Simplify the expression .
Pr 2 Solve the equation .
Pr 3 Solve the equation .
Pr 4 Solve the following equations:
a) . b) .
Pr 5 Find all values of for which the equation is valid.
Pr 6 Rewrite the expression as a sum of terms with rational exponents.
Pr 7 Solve the equation .
Pr 8 Solve the equation .
Pr 9 Solve the equation .
Pr 10 Solve the equation .
Pr 11 Solve the equation .
Go to the Solutions.
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