To find: The values of x for the expression , where x is defined as real number.
The values of x in defined as a real numbers.
The expression is .
The expression is defined as a real number when polynomial function is greater than or equal to zero.
The square roots of any function is not defined for negative values of function.
On further simplification,
The factors of the left-hand side are x, and these are zero when .
Two possible values of x give the corresponding intervals of inequality , and .
Now, make a table indicating the sign of each factor on each interval,
From the above sign table, the inequality is satisfied on the intervals and the end points of intervals and .
So the solution of given expression is all x-values, in between to , for which the expression is defined as a real number.
Thus, the values of x in defined as a real numbers.
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