Răspuns
Explicație pas cu pas:
[tex]3^{x^2+x}=9\\3^{x^2+x}=3^2\\x^2+x=2\\x^2+x-2=0\\\Delta=1+4\cdot 2=1+8=9\Rightarrow \sqrt{\Delta}=3\\x_1= \dfrac{-1+3}{2}=\dfrac{2}{2}=1\\x_2=\dfrac{-1-3}{2}=\dfrac{-4}{2}=-2\\S:x\in \{-2,1\}[/tex]
[tex]\sqrt{2x^2+1}=1\\2x^2+1=1\\2x^2=0\\x^2=0\\x=0[/tex]
[tex]\lg^2x-3\lg x+2=0\\\lg x\stackrel{not}{=} t\\t^2-3t+2=0\\\Delta=9-4\cdot 2=9-8=1\\t_1=\dfrac{3+1}{2}=\dfrac{4}{2}=2\\t_2=\dfrac{3-1}{2}=\dfrac{2}{2}=1\\\lg x=2\Rightarrow x=100\\\lg x=1\Rightarrow x=10\\S:x\in \{10,100\}[/tex]
[tex]\log_2 x=4\\x=2^4=16[/tex]
