find the real solutions of the following radical equation.

\d = \sqrt{13d - 36}\

\d = ?, \

enter the smallest solution first.

Question

find the real solutions of the following radical equation.

\d = \sqrt{13d - 36}\

\d = ?,  \

enter the smallest solution first.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Equations", "Solving Radical Equations", "Extraneous Solutions" ], "new_concepts": [], "current_concepts": [ "Radical Equations", "Solving Radical Equations", "Extraneous Solutions", "Quadratic Equations" ] } ## Square both sides of the equation $$ \begin{aligned} d &= \sqrt{13d - 36} \ d^2 &= 13d - 36 \end{aligned} $$ ## Solve the quadratic equation $$ \begin{aligned} d^2 - 13d + 36 &= 0 \ (d - 4)(d - 9) &= 0 \ d = 4 \quad &\text{or} \quad d = 9 \end{aligned} $$ ## Verify solutions in the original equation $$ \begin{aligned} \text{For } d = 4: \quad 4 &= \sqrt{13(4) - 36} = \sqrt{52 - 36} = \sqrt{16} = 4 \quad (\text{True}) \ \text{For } d = 9: \quad 9 &= \sqrt{13(9) - 36} = \sqrt{117 - 36} = \sqrt{81} = 9 \quad (\text{True}) \end{aligned} $$ Find the real solutions of the following radical equation. $d = \sqrt{13d - 36}$ $d =$ 4, 9 Enter the smallest solution first. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Radical Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Square both sides of the equation

Solve the quadratic equation

Verify solutions in the original equation

Answer: