Question

[Nguyễn Hương]

tìm x biết

a/ x² . (x+2)+4(x+2)=0

b/ 3^x+2 +4.3^x+1 +3^x-1 = 6⁶

Answer 1

[Mashiro Shiina]

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) \(3^{x+2}+4.3^{x+1}+3^{x-1}=6^6\)

\(\Rightarrow3^x.9+3^x.12+3^x.\dfrac{1}{3}=46656\)

\(\Rightarrow3^x\left(9+12+\dfrac{1}{3}\right)=46656\Leftrightarrow3^x.\dfrac{64}{3}=46656\Leftrightarrow3^x=2187\Leftrightarrow x=7\)

Answer 2

[Hiiiii~]

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) \(3^{x+2}+4.3^{x+1}+3^{x-1}=6^6\)

\(\Leftrightarrow3^{x-1+3}+4.3^{x-1+2}+3^{x-1}=6^6\)

\(\Leftrightarrow3^{x-1}\left(3^3+4.3^2+3\right)=6^6\)

\(\Leftrightarrow3^{x-1}.66=6^6\)

\(\Leftrightarrow3^{x-1}=\dfrac{6^6}{66}\)

\(\Leftrightarrow3^x-3=\dfrac{7779}{11}\)

\(\Leftrightarrow3^x=\dfrac{7809}{11}\)

Tìm x rồi kết luận