value: 1

the product of two consecutive positive integers is 72. find the two positive integers.

a. 8 and -9
b. -8 and -9
c. -8 and 9
d. 8 and 9

Question

value: 1

the product of two consecutive positive integers is 72. find the two positive integers.

a. 8 and -9
b. -8 and -9
c. -8 and 9
d. 8 and 9

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": [ "Quadratic Equations" ], "new_concepts": [ "Consecutive Integers" ], "current_concepts": [ "Quadratic Equations", "Consecutive Integers" ] } ## Set up the quadratic equation Using the *Quadratic Equations* knowledge point $$ \begin{aligned} &x(x + 1) = 72 \ &x^2 + x - 72 = 0 \end{aligned} $$ ## Solve the quadratic equation Using the *Quadratic Equations* knowledge point $$ \begin{aligned} &(x + 9)(x - 8) = 0 \ &x = -9 \quad \text{or} \quad x = 8 \end{aligned} $$ ## Determine the positive integer solutions Using the *Quadratic Equations* knowledge point $$ \begin{aligned} &\text{Since } x \text{ must be a positive integer:} \ &x = 8 \ &x + 1 = 9 \end{aligned} $$

a. 8 and -9

b. -8 and -9

c. -8 and 9

d. 8 and 9

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

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Question

Explanation:

Set up the quadratic equation

Solve the quadratic equation

Determine the positive integer solutions

Answer: