Va rog pentru C imi da valori ciudate și a-si dori cum sa fac ca sa imi dea un rezultat.​

Răspuns:

Explicație pas cu pas:

[tex]\displaystyle\texttt{Se aplica conditia de coliniaritate :}\\\begin{vmatrix}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{vmatrix}=0\Leftrightarrow \begin{vmatrix}1&3&1\\-1&7&1\\m+1&2m-5&1\end{vmatrix}=0\\\begin{vmatrix}1&3&1\\-1&7&1\\m+1&2m-5&1\end{vmatrix}=7-2m+5+3m+3-7m-7-2m+5+3=\\=-8m+16\\\texttt{Avem ca : }-8m+16=0\Rightarrow\boxed{m=2}[/tex]

[tex]\displaystyle A(1;3),~B(-1;7),~C(m+1;2m-5)\\ \\ A,~B,~C~-~coliniare \Rightarrow \left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right|=0\Rightarrow \left|\begin{array}{ccc}1&3&1\\-1&7&1\\m+1&2m-5&1\end{array}\right|=0\\ \\ \left|\begin{array}{ccc}1&3&1\\-1&7&1\\m+1&2m-5&1\end{array}\right|=1\cdot7\cdot1+1\cdot(-1)\cdot(2m-5)+3\cdot1\cdot(m+1)-\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-1\cdot7\cdot(m+1)-3\cdot(-1)\cdot1-1\cdot1\cdot(2m-5)=\\ \\ =7-2m+5+3m+3-7m-7+3-2m+5=-8m+16[/tex]

[tex]\displaystyle \left|\begin{array}{ccc}1&3&1\\-1&7&1\\m+1&2m-5&1\end{array}\right|=0\Rightarrow -8m+16=0\Rightarrow -8m=0-16\Rightarrow \\ \\ \Rightarrow -8m=-16 \Rightarrow 8m=16 \Rightarrow m=\frac{16}{8} \Rightarrow m=2[/tex]