Question

 resolva a seguinte equação exponencial 2^(x² - 7x  + 12) = 1 

Answer 1

$\mathtt{2^{(x^{2} - 7x + 12)}=1}$

$\mathtt{2^{(x^{2} - 7x + 12)}=2^{0}}$

$\mathtt{x^{2} - 7x + 12=0}$


Resolvendo por Bháskara


$\mathtt{\Delta=b^{2}-4\cdot a\cdot c}$

$\mathtt{\Delta=(-7)^{2}-4\cdot 1\cdot 12}$

$\mathtt{\Delta=49-48}$

$\mathtt{\Delta=1\quad \qquad \sqrt{1}=1}$


Encontrando as raízes


$\mathtt{x'=\dfrac{-(-7)+1}{2}}$

$\mathtt{x'=}\dfrac{8}{2}$

$\mathtt{x'= 4}$


$\mathtt{x''=\dfrac{-(-7)-1}{2}}$

$\mathtt{x''=}\dfrac{6}{2}$

$\mathtt{x''= 3}$


$\boxed{\begin{array}{c} \mathsf{\mathsf{S=\left \{ 3,4 \right \}}}\end{array}}$


Bons estudos! :)