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a) \(\sqrt{16}+\sqrt{225}.\sqrt{9}=4+15.3=4+45=49\)
b) \(\sqrt{\dfrac{10000}{400}}+\sqrt{\left(-3\right)^2}.\sqrt{6^4}=\dfrac{100}{20}+\sqrt{9}.\sqrt{36^2}=5+3.36=5+108=113\)
\(\frac{1}{4}:x=-\frac{7}{20}\)
\(x=\frac{1}{4}:-\frac{7}{20}\)
\(x=-\frac{5}{7}\)
\(\frac{3}{4}+\frac{1}{4}\div x=\frac{2}{5}\)
\(\Rightarrow\frac{1}{4}\div x=-\frac{7}{20}\)
\(\Rightarrow x=\frac{1}{4}\div\left(-\frac{7}{20}\right)\)
\(\Rightarrow x=-\frac{5}{7}\)
\(\dfrac{16}{x-\dfrac{1}{3}}=\dfrac{x-\dfrac{1}{3}}{4}\left(x\ne\dfrac{1}{3}\right)\\ \Leftrightarrow\left(x-\dfrac{1}{3}\right)^2=16\cdot4=64\\ \Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=8\\x-\dfrac{1}{3}=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{25}{3}\\x=-\dfrac{23}{3}\end{matrix}\right.\)
a) \(\left(x-\dfrac{1}{2}\right)^2=0\)
\(\Rightarrow x-\dfrac{1}{2}=0\)
\(\Rightarrow x=\dfrac{1}{2}\)
b) \(\left(x-2\right)^2=1\)
\(\Rightarrow x-2=1\)
\(\Rightarrow x=3\)
c) \(\left(2x-1\right)^3=-8\)
\(\Rightarrow\left(2x-1\right)^3=\left(-2\right)^3\)
\(\Rightarrow2x-1=-2\)
\(\Rightarrow2x=-1\)
\(\Rightarrow x=\dfrac{-1}{2}\)
d) \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)
\(\Rightarrow\left(x+\dfrac{1}{2}\right)^2=\left(\dfrac{1}{4}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{4}\\x+\dfrac{1}{2}=-\dfrac{1}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-1}{4}\\x=\dfrac{-3}{4}\end{matrix}\right.\).
a , \(\left(x-\dfrac{1}{2}\right)^2=0\)
<=> \(x-\dfrac{1}{2}=0\Rightarrow x=\dfrac{1}{2}\)
b , \(\left(x-2\right)^2=1\Rightarrow\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
c , \(\left(2x-1\right)^3=-8\Rightarrow2x-1=-2\Rightarrow x=\dfrac{-1}{2}\)
d , \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{4^2}\)
<=> \(\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{4}\\x+\dfrac{1}{2}=\dfrac{-1}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{4}\\x=\dfrac{-3}{4}\end{matrix}\right.\)
(-3)^x/81=-27
(-3)^x:(-3)^4=(-3)^3
(-3)^x=(-3)^3.(-3)^4
(-3)^x=(-3)^7
suy ra x=7
vậy x=7
\(\frac{\left(-3\right)^x}{81}=-27\)
\(\Rightarrow\left(-3\right)^x=-27.81=-2187\)
\(\Rightarrow\left(-3\right)^x=\left(-3\right)^7\)
\(\Rightarrow x=7\)
