[tex]\mathrm{Seja}\ f:\mathbb{R}\to\mathbb{R}\ \mathrm{tal\ que}\ f(x)=x^2-7x+11.[/tex]
[tex]\mathrm{Seja}\ g:\mathbb{R}\to\mathbb{R}\ \mathrm{tal\ que}\ g(x)=3x-5.[/tex]
[tex]\mathrm{Sejam}\ a\ \mathrm{e}\ b\ (a<b)\ \mathrm{os\ valores\ de}\ x\ \mathrm{tais\ que}\ f(x)=g(x).[/tex]
[tex]f(x)=g(x)\Longrightarrow x^2-7x+11=3x-5\Longrightarrow x^2-10x+16=0[/tex]
[tex]\Longrightarrow x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4(1)(16)}}{2(1)}=\dfrac{10\pm\sqrt{36}}{2}=5\pm3[/tex]
[tex]\Longrightarrow \boxed{a=2}\ \text{e}\ \boxed{b=8}[/tex]
[tex]\mathrm{Se}\ a\ \text{e}\ b\ \mathrm{s\tilde{a}o\ termos\ de\ uma\ PG\ com}\ n=3\ \text{e}\ q>3\text{:}[/tex]
[tex]a\ \mathrm{\acute{e}\ o\ menor\ termo}\Longrightarrow \{a,b,c\}\Longrightarrow \{2,8,c\}[/tex]
[tex]q=\dfrac{8}{2}\Longrightarrow q=4\Longrightarrow q>3[/tex]
[tex]\Longrightarrow \{2,8,c\}\Longrightarrow \{2,8,32\}[/tex]
[tex]\mathrm{Soma\ dos\ termos}\Longrightarrow S=2+8+32[/tex]
[tex]\Longrightarrow S=42\Longrightarrow\ \boxed{S<45}\ \blacksquare[/tex]
[tex]\mathbf{A\ afirmativa\ \acute{e}\ verdadeira.}[/tex]
