Lời giải:
Theo định lý Viet:
$x_1+x_2=\frac{-9}{2}$
$x_1x_2=\frac{-5}{2}$
Khi đó:
\(M=\frac{1}{x_1^2}-\frac{1}{x_2^2}=\frac{x_2^2-x_1^2}{x_1^2x_2^2}=\frac{(x_2-x_1)(x_2+x_1)}{(x_1x_2)^2}\\
=(x_2-x_1).\frac{-9}{2}: (\frac{-5}{2})^2=\frac{18}{25}(x_1-x_2)\)
\(=\frac{18}{25}\sqrt{(x_1+x_2)^2-4x_1x_2}=\frac{18}{25}\sqrt{(\frac{-9}{2})^2-4.\frac{-5}{2}}=\frac{99}{25}\)