Canonical URI: https://w3id.org/kmath/textbook_solution/visang_solution_p159_workbook_p140_06
| rdf:type | math:TextbookSolution |
|---|---|
| rdfs:label | 비상 p140 수학 익힘책 IV-06 풀이 |
| rdfs:comment | 비상 공통수학1 정답 및 해설 p159의 수학 익힘책 p140 IV-06 풀이. |
| math:answerText | \(a=-2, b=-3\) |
| math:explanationText | \[ \begin{pmatrix}\alpha^2+\beta^2&2(\alpha+\beta)\\0&2\alpha\beta\end{pmatrix} = \begin{pmatrix}10&4\\0&2\alpha\beta\end{pmatrix} \] 이때 \(\alpha^2+\beta^2=10,\ \alpha+\beta=2\)이므로 \(\alpha\beta=-3\). 이차방정식 \(x^2+ax+b=0\)의 두 실근이 \(\alpha,\ \beta\)이므로 \[ a=-(\alpha+\beta)=-2,\quad b=\alpha\beta=-3 \] |
| math:mappingConfidence | 1.0 |
| math:pageStart | 159 |
| math:problem | textbook_problem:visang_workbook_p140_06 |
| math:reviewStatus | reviewed |
| math:solutionKind | worked_solution |
| math:usesSolutionPattern | solution_pattern:matrix_equality_component_equations |
| math:usesSolutionPattern | solution_pattern:roots_coefficients_symmetric_expression |