[tex]\mathtt{2^{(x^{2} - 7x + 12)}=1}\\\\[/tex]
[tex]\mathtt{2^{(x^{2} - 7x + 12)}=2^{0}}\\\\[/tex]
[tex]\mathtt{x^{2} - 7x + 12=0}\\\\[/tex]
Resolvendo por Bháskara
[tex]\mathtt{\Delta=b^{2}-4\cdot a\cdot c}\\\\[/tex]
[tex]\mathtt{\Delta=(-7)^{2}-4\cdot 1\cdot 12}\\\\[/tex]
[tex]\mathtt{\Delta=49-48}\\\\[/tex]
[tex]\mathtt{\Delta=1\quad \qquad \sqrt{1}=1}\\\\[/tex]
Encontrando as raízes
[tex]\mathtt{x'=\dfrac{-(-7)+1}{2}}\\\\[/tex]
[tex]\mathtt{x'=}\dfrac{8}{2}\\\\[/tex]
[tex]\mathtt{x'= 4}\\\\[/tex]
[tex]\mathtt{x''=\dfrac{-(-7)-1}{2}}\\\\[/tex]
[tex]\mathtt{x''=}\dfrac{6}{2}\\\\[/tex]
[tex]\mathtt{x''= 3}\\\\[/tex]
[tex]\boxed{\begin{array}{c} \mathsf{\mathsf{S=\left \{ 3,4 \right \}}}\end{array}}[/tex]
Bons estudos! :)
