Question

2 la puterea 6-x patrat = 2 la puterea x

Answer 1

$2^{6-x^2}=2^x \\\\ 6-x^2=x \\\\ -x^2-x+6=0 \ \ \ \ \textless \ =\ \textgreater \ \ \ \ x^2+x-6=0 \\\\\\ \Delta=1-4*(-6)= 1+24 \to 25 \\\\ x_1=\frac{-1+5}{2} \to 2 \\\\\\ x_2=\frac{-1-5}{2} \to -3 \\\\\\ Verificare: \\ Pt \ x \to 2 \\\\\ 2^{6-2^2}=2^{2} \\\\ 2^{6-4}=2^2 \ \ \ 'A' \\\\\\ Pt \ x \to -3 \\\\ 2^{6-(-3)^2}=2^{-3} \\\\ 2^{6-9}= 2^{-3} \ \ \ 'A' \\\\\\ S \ \in \{ -3;2 \}$