Estude! Com Prof. Caju

Problema Proposto
29 - A, C, M e B são pontos colineales e
consecutivos. Se AC = CB , AM.AB = 8 e
[tex3]\frac{1}{2MB} = \frac{2}{AM}-\frac{1}{AC}[/tex3]
Calcular: MB

[tex3]\mathsf{
AC = x\\
CM = y\\
CB = x\\
MB=x-y\\
(x+y).2x = 8 \implies x(x+y)=4\\
\frac{1} {2MB} = \frac{2}{x+y}-\frac{1}{x}\implies \frac{1}{2MB} = \frac{2x-x-y}{x(x+y)}\implies\\
x(x+y)=2MB(x-y)\implies 2MB^2=4\therefore \boxed{\color{red} MB =\sqrt2}

}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\mathsf{
AC = x\\
CM = y\\
CB = x\\
MB=x-y\\
(x+y).2x = 8 \implies x(x+y)=4\\
\frac{1} {2MB} = \frac{2}{x+y}-\frac{1}{x}\implies \frac{1}{2MB} = \frac{2x-x-y}{x(x+y)}\implies\\
x(x+y)=2MB(x-y)\implies 2MB^2=4\therefore \boxed{\color{red} MB =\sqrt2}

}[/tex3]