Question

Dada a equação 3²^ -4•3^ +3=0
,Qual a soma entre suas raízes?
(^ significa x )

Answer 1

$3^{2x}-4.3^x+3=0 \\ \\ colocar~~3^x=y \\ \\ y^2-4y+3=0 \\ a=1 \\ b=-4 \\ c=3 \\ \\ \Delta=b^2-4ac \\ \Delta=(-4)^2-4(1)(3) \\ \Delta=16-12 \\ \Delta=4 \\ \\y= \frac{-b\pm \sqrt{\Delta} }{2a} =~~ \frac{-(-4)\pm \sqrt{4} }{2} = \frac{~4\pm2}{2} \\ \\ y'= \frac{4+2}{2} = \frac{6}{2} =3 \\ \\ y"= \frac{4-2}{2} = \frac{2}{2} =1$

$se \\ 3^x=y ~ \\ ~p/y=3 \\ 3^x=3 \\ 3^x=3^1 \\ x=1 \\ \\ p/y=1 \\ 3^x=1 \\ 3^x=3^0 ~~( todo~~ n\'umero~~~elevado~~a~~zero=1) \\ x=0 \\ \\ logo ~~a~~soma~~das~~ra\'izes~~1+0=1$