a)\(x^2\left(x+2\right)+4\left(x+2\right)=0\)
\(\Rightarrow\left(x^2+4\right)\left(x+2\right)=0\)
\(x^2+4>0\Leftrightarrow x+2=0\Leftrightarrow x=-2\)
b) \(3^{x+2}+4.3^{x+1}+3^{x-1}=6^6\)
\(\Rightarrow3^x.9+3^x.12+3^x.\dfrac{1}{3}=46656\)
\(\Rightarrow3^x\left(9+12+\dfrac{1}{3}\right)=46656\Leftrightarrow3^x.\dfrac{64}{3}=46656\Leftrightarrow3^x=2187\Leftrightarrow x=7\)
Giải:
a) \(x^2\left(x+2\right)+4\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2+4\right)=0\)
Vì \(x^2+4>0;\forall x\)
\(\Leftrightarrow x+2=0\)
\(\Leftrightarrow x=-2\)
Vậy ..
b) \(3^{x+2}+4.3^{x+1}+3^{x-1}=6^6\)
\(\Leftrightarrow3^{x-1+3}+4.3^{x-1+2}+3^{x-1}=6^6\)
\(\Leftrightarrow3^{x-1}\left(3^3+4.3^2+3\right)=6^6\)
\(\Leftrightarrow3^{x-1}.66=6^6\)
\(\Leftrightarrow3^{x-1}=\dfrac{6^6}{66}\)
\(\Leftrightarrow3^x-3=\dfrac{7779}{11}\)
\(\Leftrightarrow3^x=\dfrac{7809}{11}\)
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