Question

9 la puterea 2x+1 minus 3 la puterea x+1 minus 6 = 0
Dau 60 pct!!!!

Answer 1

$9^{2x+1}-3^{x+1}-6=0$
$3^{2(2x+1)}-3^{x+1}-6=0$
$(3^{2x+1})^2-3^{x+1}-6=0$
Notam $3^{2x+1} = y$
$y^2-y-6=0$
Δ=b²-4ac= 25
$y_{1,2}= \frac{-b+- \sqrt{delta} }{2a}$
[tex]y_1= \frac{1+5}{2} =3 [/tex]
[tex]y_2= \frac{1-5}{2} =-2 [/tex]
$3^{2x+1} = 3$
$2x+1=1=\ \textgreater \ x=0$
$3^{2x+1}= -2$
-2<0 ==> Ø
==> S={0}