Answer :
[tex]:\implies\bf\:m+n=18\:\longrightarrow\:(I)[/tex]
[tex]:\implies\sf\:2mn=-24\:\longrightarrow\:(II)[/tex]
[tex]:\implies\bf\:mn=-12\:\longrightarrow\:(III)[/tex]
Answer - A :
[tex]:\implies\tt\:\dfrac{5}{3m}+\dfrac{5}{3n}[/tex]
[tex]:\implies\tt\:\dfrac{15(m+n)}{9(mn)}[/tex]
[tex]:\implies\tt\:\dfrac{15(18)}{9(-12)}[/tex]
[tex]:\implies\tt\:-\dfrac{15}{6}[/tex]
[tex]:\implies\:\boxed{\bf{\purple{-\dfrac{5}{2}}}}[/tex]
Answer - B :
[tex]:\implies\tt\:\dfrac{4}{m^2}+\dfrac{4}{n^2}[/tex]
[tex]:\implies\tt\:\dfrac{4(m^2+n^2)}{(mn)^2}[/tex]
[tex]:\implies\tt\:\dfrac{4(m^2+2mn+n^2-2mn)}{(mn)^2}[/tex]
[tex]:\implies\tt\:\dfrac{4[(m+n)^2-2mn]}{(mn)^2}[/tex]
[tex]:\implies\tt\:\dfrac{4[(18)^2-(-24)]}{(-12)^2}[/tex]
[tex]:\implies\tt\:\dfrac{4(324+24)}{144}[/tex]
[tex]:\implies\tt\:\dfrac{348}{36}[/tex]
[tex]:\implies\:\boxed{\bf{\orange{\dfrac{29}{3}}}}[/tex]
