Sabendo que a distância entre os pontos A(-1,2,3) e B(1,-1,m) é igual a 7, calcular o valor de m.
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Solução!
![\sqrt{(1+1)^{2} +(-1-2)^{2}+(m-3)^{2}} =7\\\\\\
\sqrt{(2)^{2} +(-3)^{2}+(m-3)^{2}} =7\\\\\\
\sqrt{4 +9+m^{2} -6m+9} =7\\\\\\
(\sqrt{4 +9+m^{2} -6m+9})^{2} =(7)^{2} \\\\\\
4 +9+m^{2} -6m+9 =49 \\\\\\
m^{2} -6m+22-49=0\\\\\
m^{2} -6m+27=0](https://tex.z-dn.net/?f=+%5Csqrt%7B%281%2B1%29%5E%7B2%7D+%2B%28-1-2%29%5E%7B2%7D%2B%28m-3%29%5E%7B2%7D%7D+%3D7%5C%5C%5C%5C%5C%5C%0A+%5Csqrt%7B%282%29%5E%7B2%7D+%2B%28-3%29%5E%7B2%7D%2B%28m-3%29%5E%7B2%7D%7D+%3D7%5C%5C%5C%5C%5C%5C%0A+%5Csqrt%7B4+%2B9%2Bm%5E%7B2%7D+-6m%2B9%7D+%3D7%5C%5C%5C%5C%5C%5C%0A%28%5Csqrt%7B4+%2B9%2Bm%5E%7B2%7D+-6m%2B9%7D%29%5E%7B2%7D++%3D%287%29%5E%7B2%7D+%5C%5C%5C%5C%5C%5C%0A4+%2B9%2Bm%5E%7B2%7D+-6m%2B9++%3D49+%5C%5C%5C%5C%5C%5C%0Am%5E%7B2%7D+-6m%2B22-49%3D0%5C%5C%5C%5C%5C%0Am%5E%7B2%7D+-6m%2B27%3D0%0A "\sqrt{(1+1)^{2} +(-1-2)^{2}+(m-3)^{2}} =7\\\\\\
\sqrt{(2)^{2} +(-3)^{2}+(m-3)^{2}} =7\\\\\\
\sqrt{4 +9+m^{2} -6m+9} =7\\\\\\
(\sqrt{4 +9+m^{2} -6m+9})^{2} =(7)^{2} \\\\\\
4 +9+m^{2} -6m+9 =49 \\\\\\
m^{2} -6m+22-49=0\\\\\
m^{2} -6m+27=0")
![m= \dfrac{-(-6)\pm \sqrt{(-6)^{2}-4.1.-27 } }{2.1}\\\\\\\\\ m= \dfrac{6\pm \sqrt{36+108} }{2}\\\\\\\ m= \dfrac{6\pm \sqrt{144} }{2}\\\\\\\ m= \dfrac{6\pm 12 }{2}\\\\\\\
m_{1}= \dfrac{6+12}{2}= \dfrac{18}{2}=9\\\\\\\
m_{2}= \dfrac{6-12}{2}= \dfrac{-6}{2}=-3\\\\\\\\\\\\\
\boxed{Resposta:m_{1}=9~~e~~m_{2}=-3}](https://tex.z-dn.net/?f=m%3D+%5Cdfrac%7B-%28-6%29%5Cpm+%5Csqrt%7B%28-6%29%5E%7B2%7D-4.1.-27+%7D+%7D%7B2.1%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C+m%3D+%5Cdfrac%7B6%5Cpm+%5Csqrt%7B36%2B108%7D+%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5C+m%3D+%5Cdfrac%7B6%5Cpm+%5Csqrt%7B144%7D+%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5C+m%3D+%5Cdfrac%7B6%5Cpm+12+%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5C+%0Am_%7B1%7D%3D+%5Cdfrac%7B6%2B12%7D%7B2%7D%3D+%5Cdfrac%7B18%7D%7B2%7D%3D9%5C%5C%5C%5C%5C%5C%5C%0Am_%7B2%7D%3D+%5Cdfrac%7B6-12%7D%7B2%7D%3D+%5Cdfrac%7B-6%7D%7B2%7D%3D-3%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3Am_%7B1%7D%3D9%7E%7Ee%7E%7Em_%7B2%7D%3D-3%7D+++%0A "m= \dfrac{-(-6)\pm \sqrt{(-6)^{2}-4.1.-27 } }{2.1}\\\\\\\\\ m= \dfrac{6\pm \sqrt{36+108} }{2}\\\\\\\ m= \dfrac{6\pm \sqrt{144} }{2}\\\\\\\ m= \dfrac{6\pm 12 }{2}\\\\\\\
m_{1}= \dfrac{6+12}{2}= \dfrac{18}{2}=9\\\\\\\
m_{2}= \dfrac{6-12}{2}= \dfrac{-6}{2}=-3\\\\\\\\\\\\\
\boxed{Resposta:m_{1}=9~~e~~m_{2}=-3}")
Boa noite!
Bons estudos!
Solução!
Boa noite!
Bons estudos!
willjonnas:
Obrigado
De nada! Boa noite1
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