Question

2^(x^2-6x+12 )=8



Obs: com a conta, pls

Answer 1

Resposta:

x=3

Explicação passo a passo:

2^(x²-6x+12)=8

fatorar 8

8|2

4|2

2|2

1

8=2.2.2=2³

2^(x²-6x+12)=2^3, como as base são iguais igualam-se os expoentes

x²-6x+12=3

x²-6x+12-3=0

x²-6x+9=0

$\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~x^{2}-6x+9=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=-6~e~c=9\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-6)^{2}-4(1)(9)=36-(36)=0\\\\C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-6)-\sqrt{0}}{2(1)}=\frac{6-0}{2}=\frac{6}{2}=3\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-6)+\sqrt{0}}{2(1)}=\frac{6+0}{2}=\frac{6}{2}=3\\\\S=\{3,~3\}$

x=x'=x''=3