tìm x, biết a) (x-1) ²=(x-1)^4 b) -5+|3x-1|+6=|-4|
1 câu trả lời
Đáp án:$a)S=\{\ 0;1;2 \}$
$b)S=\{\ \dfrac{-2}{3};\dfrac{4}{3} \}$
Giải thích các bước giải:
$a)(x-1)^2=(x-1)^4$
$(x-1)^4-(x-1)^2=0$
$(x-1)^2.[(x-1)^2-1]=0$
\(\Leftrightarrow\left[ \begin{array}{l}(x-1)^2=0\\(x-1)^2-1=0\end{array} \right.\)
\(\Leftrightarrow\left[ \begin{array}{l}(x-1)^2=0\\(x-1)^2-1=0\end{array} \right.\)
\(\Leftrightarrow\left[ \begin{array}{l}x=1\\x=0\\x=2\end{array} \right.\)
Vậy $S=\{\ 0;1;2 \}$
$b)-5+|3x-1|+6=|-4|$
$|3x-1|+1=4$
$|3x-1|=3$
\(\Leftrightarrow\left[ \begin{array}{l}3x-1=3\\3x-1=-3\end{array} \right.\)
\(\Leftrightarrow\left[ \begin{array}{l}x=\dfrac{4}{3}\\x=\dfrac{-2}{3}\end{array} \right.\)
Vậy $S=\{\ \dfrac{-2}{3};\dfrac{4}{3} \}$
