which equation can be rewritten as $x + 4 = x^2$? assume $x 0$.

* $\sqrt{x} + 2 = x$
* $\sqrt{x + 2} = x$
* $\sqrt{x + 4} = x$
* $\sqrt{x^2 + 16} = x$

Question

which equation can be rewritten as $x + 4 = x^2$? assume $x > 0$.

* $\sqrt{x} + 2 = x$
* $\sqrt{x + 2} = x$
* $\sqrt{x + 4} = x$
* $\sqrt{x^2 + 16} = x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Radical Equations", "Radical Equation Definition" ], "new_concepts": [], "current_concepts": [ "Solving Radical Equations", "Radical Equation Definition" ] } ## Analyze the target equation Using the *Solving Radical Equations* and *Radical Equation Definition* knowledge points $$ \begin{aligned} &x + 4 = x^2 \quad (\text{for } x > 0) \end{aligned} $$ ## Test the given options by squaring both sides Using the *Solving Radical Equations* knowledge point $$ \begin{aligned} &\text{Option 1: } \sqrt{x} + 2 = x \implies \sqrt{x} = x - 2 \implies x = (x-2)^2 = x^2 - 4x + 4\ &\text{Option 2: } \sqrt{x+2} = x \implies x + 2 = x^2\ &\text{Option 3: } \sqrt{x+4} = x \implies x + 4 = x^2\ &\text{Option 4: } \sqrt{x^2+16} = x \implies x^2 + 16 = x^2 \implies 16 = 0 \end{aligned} $$ ## Identify the matching equation Using the *Solving Radical Equations* knowledge point $$ \begin{aligned} &\sqrt{x+4} = x \implies x + 4 = x^2 \end{aligned} $$

(A) $\sqrt{x} + 2 = x$

(B) $\sqrt{x+2} = x$

(C) $\sqrt{x+4} = x$

(D) $\sqrt{x^2+16} = x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Radical Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the target equation

Test the given options by squaring both sides

Identify the matching equation

Answer: