Question

A distância entre os pontos A(2,1) e B (x,3) é raiz de 8 determine o valor de x

Answer 1

$\Large\boxed{\begin{array}{l}\sf d_{A,B}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\sf \sqrt{8}=\sqrt{(x-2)^2+(3-1)^2}\\\sf\sqrt{(x-1)^2+4}=\sqrt{8}\\\sf(\sqrt{(x-1)^2+4})^2=(\sqrt{8})^2\\\sf (x-1)^2+4=8\\\sf(x-1)^2=8-4\\\sf(x-1)^2=4\\\sf x-1=\pm\sqrt{4}\\\sf x-1=\pm2\\\sf x-1=2\implies x=3\\\sf x-1=-2\implies x=-1\end{array}}$