EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note::

• In order to solve for x, you must isolate x.

• In order to isolate x, you must remove it from under the radical.

• If there is just one radical in the equation, isolate the radical.

• Then raise both sides of the equation to a power equal to the index of the radical.

• With these types of equations, sometimes there are extraneous solutions; therefore, you must check your answers.

• If the index of the radical is even, many times there will be a restriction on the values of x.

Problem2.2e:

Solution:

• A positive number (left side) cannot equal a negative number (right side); therefore, there is no solution.

• Suppose you did not catch this at first and worked the problem. You would catch your error in the check.

• Divide both sides of the original equation by 5.

• Square both sides of the equation.

• Subtract 1 from both sides of the equation.

• Check the solution by substituting 0 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.

Left side:

Right Side: Since the left side of the original equation does not equal the

right side of the original equation when 0 is substituted for x, thenx=0

is not a solution. Since it was the only solution you found, then the

conclusion is that there is not a solution to the problem.

You can also check the answer by graphing

(the left side of the original equation minus the right side of

the original equation). Since the graph never crosses the x-axis, there

is no x-intercept. If there is no x-intercept, there is no solution.

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