What is the solution set of the equation above?
\n","rationale_html":"Choice B is correct. Subtracting 4 from both sides of isolates the radical expression on the left side of the equation as follows:
. Squaring both sides of
yields
. This equation can be rewritten as a quadratic equation in standard form:
. One way to solve this quadratic equation is to factor the expression
by identifying two numbers with a sum of
and a product of
. These numbers are
and 1. So the quadratic equation can be factored as
. It follows that 5 and
are the solutions to the quadratic equation. However, the solutions must be verified by checking whether 5 and
satisfy the original equation,
. When
, the original equation gives
, or
, which is false. Therefore,
does not satisfy the original equation. When
, the original equation gives
, or
, which is true. Therefore,
is the only solution to the original equation, and so the solution set is
.
Choices A, C, and D are incorrect because each of these sets contains at least one value that results in a false statement when substituted into the given equation. For instance, in choice D, when 0 is substituted for x into the given equation, the result is , or
. This is not a true statement, so 0 is not a solution to the given equation.
\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.638000+00:00","source_updated_at":"2023-08-02T20:25:59.638000+00:00","options":[{"label":"A","content_html":"