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a) \(\dfrac{27}{2}\cdot7,5+\dfrac{27}{2}\cdot2,5-150\)
\(=\dfrac{27}{2}\cdot\left(7,5+2,5\right)-150\)
\(=\dfrac{27}{2}\cdot10-150\)
\(=135-150\)
\(=-15\)
b) \(3^3\cdot\dfrac{18}{5}-3^3\cdot2\dfrac{2}{5}-3^3\cdot\dfrac{6}{5}\)
\(=3^3\cdot\dfrac{18}{5}-3^3\cdot\dfrac{12}{5}-3^3\cdot\dfrac{6}{5}\)
\(=3^3\cdot\left(\dfrac{18}{5}-\dfrac{12}{5}-\dfrac{6}{5}\right)\)
\(=3^3\cdot\left(\dfrac{18}{5}-\dfrac{18}{5}\right)\)
\(=3^3\cdot0\)
\(=0\)
\(\left|x+\frac{1}{3}\right|+\frac{4}{5}=\left|-3,2+\frac{2}{5}\right|+\left(27-\frac{3}{5}\right)\left(27-\frac{3^2}{6}\right)...\left(27-\frac{3^5}{9}\right)...\left(27-\frac{3^{2010}}{2014}\right)\)
\(\Leftrightarrow\left|x+\frac{1}{3}\right|+\frac{4}{5}=\frac{14}{5}+\left(27-\frac{3^2}{6}\right)\left(27-\frac{3^3}{7}\right)...\left(27-27\right)...\left(27-\frac{3^{2010}}{2014}\right)\)
\(\Leftrightarrow\left|x+\frac{1}{3}\right|+\frac{4}{5}=\frac{14}{5}\)
\(\Leftrightarrow\left|x+\frac{1}{3}\right|=2\)
\(\Rightarrow\hept{\begin{cases}x+\frac{1}{3}=2\\x+\frac{1}{3}=-2\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{5}{3}\\x=-\frac{7}{3}\end{cases}}}\)
bạn ơi, có một chỗ chưa chuẩn .bạn kiểm tra lại giú mình. chỗ vế trái bạn thiếu \(\left(27-\frac{3}{5}\right)\). bạn bổ sung vào cho đúng nhé. dù sao vẫn cảm ơn bạn.
Vũ Hồng Linh bạn check lại bài đầu dùm =_="
\(\left[-\frac{1}{3}\right]^3\cdot x=\frac{1}{81}\)
\(\Leftrightarrow x=\frac{1}{81}:\left[-\frac{1}{3}\right]^3\)
\(\Leftrightarrow x=\frac{1}{81}:\left[-\frac{1}{27}\right]\)
\(\Leftrightarrow x=\frac{1}{81}\cdot(-27)=-\frac{1}{3}\)
\(\left[x-\frac{1}{2}\right]^3=\frac{1}{27}\)
\(\Leftrightarrow\left[x-\frac{1}{2}\right]^3=\left[\frac{1}{3}\right]^3\)
=> Làm nốt
Mấy bài kia cũng làm tương tự
(- \(\dfrac{1}{3}\))3.\(x\) = \(\dfrac{1}{81}\)
\(x=\dfrac{1}{81}\) : (- \(\dfrac{1}{3}\))3
\(x\) = - (\(\dfrac{1}{3}\))4 :(\(\dfrac{1}{3}\))3
\(x=-\dfrac{1}{3}\)
Vậy \(x=-\dfrac{1}{3}\)
\(a)x+\left(-5\right)=-14\)
\(\Leftrightarrow x=-14-\left(-5\right)\)
\(\Leftrightarrow x=-14+5\)
\(\Leftrightarrow x=-9\)
\(b)-x+7=-23\)
\(\Leftrightarrow-x=-23+ \left(-7\right)\)
\(\Leftrightarrow-x=-30\)
\(\Leftrightarrow x=30\)
\(c)112-x=\left(-3\right).\left(-15\right)\)
\(\Leftrightarrow112-x=45\)
\(\Leftrightarrow x=112-45\)
\(\Leftrightarrow x=67\)
\(d)\left(x-15\right)-27=5^5:5^3\)
\(\Leftrightarrow\left(x-15\right)-27=5^2\)
\(\Leftrightarrow\left(x-15\right)-27=25\)
\(\Leftrightarrow x-15=52\)
\(\Leftrightarrow x=67\)
\(e)\left(2x+1\right)^2=81\)
\(\Leftrightarrow\left(2x+1\right)^2=9^2\)
\(\Leftrightarrow2x+1=9\)
\(\Leftrightarrow2x=8\)
\(\Leftrightarrow x=4\)
\(f)(x-5^3)=-27\)
\(f)(x-5^3)=-9^3\)
\(\Leftrightarrow x-5=-9\)
\(\Leftrightarrow x=-4\)
P/s: Bạn tự kết luận.
phần b nhé
(X+0,7)3=-27
(X+0,7)3=(-3)3
X+0,7=-3
X=3-0,7=2,3
Vậy...
\(\dfrac{3^{x-5}+3^{x-4}+3^{x-3}}{13}=\dfrac{27}{3^x}\)
\(\Rightarrow3^x\left(3^{x-5}+3^{x-4}+3^{x-3}\right)=27.13\)
\(\Rightarrow3^{2x}\left(3^{-5}+3^{-4}+3^{-3}\right)=351\)
\(\Rightarrow3^{2x}=6561\Rightarrow2x=8\Rightarrow x=4\)
\(\left(x-1,2\right)^2=4\)
⇔\(x^2-2.x.1,2+1,2^2=4\)
⇔\(x^2-2,4x+1,44=4\)
⇔\(x^2-2,4x=4-1,44\)
⇔\(x\left(x-2,4\right)=2,56\)
⇔\(x=2,56\) hoặc \(x-2,4=2,56\)
⇔\(x=2,56\) hoặc \(x=4,96\)
a) \(\left(x-1,2\right)^2=4=2^2\)
\(\Leftrightarrow x-1,2=4\)
\(\Leftrightarrow x=5,2\)
b) \(\left(x+1\right)^3=-125=\left(-5\right)^3\)
\(\Leftrightarrow x+1=-5\)
\(\Leftrightarrow x=-6\)
c) \(\left(x+1,5\right)^8+\left(2,7-y\right)^{10}=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+1,5=0\\2,7-y=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-1,5\\y=2,7\end{matrix}\right.\)
(x+5)3=-33
x+5=-3 =>x=-3-5=-8