EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS
- In order to solve for x, you must isolate x.
- In order to isolate x, you must remove it from under the radial.
- If there are two radicals in the equation,isolate one of the radicals.
- Then raise both sides of the equation to a power equal to the index
of the isolated radical.
- Isolate the remaining radical.
- Raise both sides of the equation to a power equal to the index of the
- You should now have a polynomial equation. Solve it.
- Remember that you did not start out with a polynomial; therefore,
there may be extraneous solutions. Therefore, you must check your
Answer:x = 36
First make a note of the fact that you cannot take the square root of a
negative number. The term is valid only if and the term
is valid if . The restricted domain must satisfy both of these constraints. Therefore, the
domain is the set of real numbers
Isolate the is already isolated, we square both sides
of the equation.
Isolate the term .
Square both sides of the equation.
The answer is 36.
Check the solution 36 by substituting 36 in the original equation for x.
If the left side of the equation equals the right side of the equation after
the substitution, you have found the correct answer.
Since the left side of the original equation equals the right side of the
original equation after we substituted our solution for x, we have verified
that the solutions is x = 36.
- Left side:
- Right Side: 10
You can also check the answer by graphing the equation:
The graph represents the right side of the original equation minus the left
side of the original equation.. The x-intercept(s) of this graph is(are) the
solution(s). Since the only x-intercept is 36, we have verified that the
only solution is 36.
If you would like to review the solution for problem 2.4d, click on Solution.
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