Determine o ccalor de X para que os pontos A(2,-3), B (x,7)e C (x,1) sejam colineares
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Resolva o determinante e iguale a zero;
![\\ det \left[\begin{array}{ccc}2&-3&1\\x&7&1\\x&1&1\end{array}\right] =0
\\
\\ 2*7*1-3*1*x+x*1*1-(x*7*1+1*1*2+-3*x*1)=0
\\
\\ 14-3x+x-(7x+2-3x)=0
\\
\\ -3x+x-7x+3x+14-2=0
\\
\\ -6x+12=0
\\
\\ 6x=12
\\
\\ x = \frac{12}{6}
\\
\\ x=2](https://tex.z-dn.net/?f=+%5C%5C+det++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26amp%3B-3%26amp%3B1%5C%5Cx%26amp%3B7%26amp%3B1%5C%5Cx%26amp%3B1%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+%3D0%0A+%5C%5C+%0A+%5C%5C+2%2A7%2A1-3%2A1%2Ax%2Bx%2A1%2A1-%28x%2A7%2A1%2B1%2A1%2A2%2B-3%2Ax%2A1%29%3D0%0A+%5C%5C+%0A+%5C%5C+14-3x%2Bx-%287x%2B2-3x%29%3D0%0A+%5C%5C+%0A+%5C%5C+-3x%2Bx-7x%2B3x%2B14-2%3D0%0A+%5C%5C+%0A+%5C%5C+-6x%2B12%3D0%0A+%5C%5C+%0A+%5C%5C+6x%3D12%0A+%5C%5C+%0A+%5C%5C+x+%3D++%5Cfrac%7B12%7D%7B6%7D+%0A+%5C%5C+%0A+%5C%5C+x%3D2 "\\ det \left[\begin{array}{ccc}2&-3&1\\x&7&1\\x&1&1\end{array}\right] =0
\\
\\ 2*7*1-3*1*x+x*1*1-(x*7*1+1*1*2+-3*x*1)=0
\\
\\ 14-3x+x-(7x+2-3x)=0
\\
\\ -3x+x-7x+3x+14-2=0
\\
\\ -6x+12=0
\\
\\ 6x=12
\\
\\ x = \frac{12}{6}
\\
\\ x=2")
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