Question

9×-4.3×+3=0 mim ajuda

Answer 1

$9^x-4.3^x+3=0 \\ \\ (3^2)^x-4.3^x+3=0 \\ \\ (3^x)^2-4.3^x+3=0 \\ \\ 3^x=Z \\ \\ Z^2 -4Z +3 = 0 \\ \\ \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\quad \to \quad \dfrac{4\pm \sqrt{16-12} }{2}= \dfrac{4\pm \sqrt{4} }{2}= \dfrac{4\pm 2 }{2}= \\ \\ \\ Z_1= \dfrac{4+2 }{2}=\dfrac{6 }{2}=3\\ \\ \\ Z_2= \dfrac{4-2 }{2}=\dfrac{2 }{2}=1 \\ \\ \\ 3^x=Z_1\quad 3^x= 3\quad \to \boxed{x=1} \\ \\ \\ 3^x=Z_1\quad 3^x= 1\quad \to \boxed{x=0}$

$9^x-4.3^x+3=0 \\ \\ \boxed{x_1= 1\qquad x_2=0 }$