7 Given that \( m+n=9 \) and \( m n=8 \), find the value of \( \begin{array}{ll}\text { (a) } m^{2}+n^{2}, & \text { (b) }(m-n)^{2}\end{array} \)
Solución de inteligencia artificial de Upstudy
Responder
Solución

¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

Respondido por UpStudy AI y revisado por un tutor profesional
Extra Insights
To solve for \( m^2 + n^2 \) and \( (m - n)^2 \) given \( m + n = 9 \) and \( mn = 8 \), we start with the first equation. We know that: \[ m^2 + n^2 = (m+n)^2 - 2mn \] Substituting in the values: \[ m^2 + n^2 = 9^2 - 2 \cdot 8 = 81 - 16 = 65 \] So, \( m^2 + n^2 = 65 \). Next, to find \( (m - n)^2 \): \[ (m - n)^2 = (m+n)^2 - 4mn \] Substituting the known values: \[ (m - n)^2 = 9^2 - 4 \cdot 8 = 81 - 32 = 49 \] Thus, \( (m - n)^2 = 49 \). The final answers are: (a) \( m^2 + n^2 = 65 \) (b) \( (m - n)^2 = 49 \)
