\
\begin{cases}
\frac{20}{t} = s \\
s^2 + t^2 = 41
\end{cases}
\
\
(s - t)^2 = ?
\

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Identities", "Systems of Equations" ], "new_concepts": [], "current_concepts": [ "Algebraic Identities", "Systems of Equations" ] } ## Express the product of the variables $$ \begin{aligned} \frac{20}{t} &= s \ st &= 20 \end{aligned} $$ ## Expand the target algebraic identity $$ (s - t)^2 = s^2 - 2st + t^2 $$ ## Substitute the known values $$ \begin{aligned} (s - t)^2 &= (s^2 + t^2) - 2(st) \ (s - t)^2 &= 41 - 2(20) \ (s - t)^2 &= 41 - 40 \ (s - t)^2 &= 1 \end{aligned} $$ 1 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Identities" ] }

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QUESTION IMAGE

Question

Explanation:

Express the product of the variables

Expand the target algebraic identity

Substitute the known values

Answer: