Question

a ) 5^-1 x 25^x = 125 ( x thuộc Z )

b) | x+ 1| + | x+2 | + |x+3| = 4x

giúp mik nha cảm ơn các ban 

Answer 1

a) \(5^{-1}.25^x=125\)

\(\Rightarrow5^{-1}.5^{2x}=5^3\)

\(\Rightarrow5^{2x-1}=5^3\)

\(\Rightarrow2x-1=3\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=2\)

Vậy \(x=2\)

b) \(|x+1|+|x+2|+|x+3|=4x\)

Vì \(\hept{\begin{cases}|x+1|\ge0\forall x\\|x+2|\ge0\forall x\\|x+3|\ge0\forall x\end{cases}}\)

\(\Rightarrow|x+1|+|x+2|+|x+3|\ge0\)

\(\Rightarrow4x\ge0\)

\(\Rightarrow x\ge0\)

\(\Rightarrow\hept{\begin{cases}x+1>0\\x+2>0\\x+3>0\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}|x+1|=x+1\\|x+2|=x+2\\|x+3|=x+3\end{cases}}\)

\(\Rightarrow\left(x+1\right)+\left(x+2\right)+\left(x+3\right)=4x\)

\(\Rightarrow3x+6=4x\)

\(\Rightarrow x=6\)

Vậy \(x=6\)