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c. \(\left|\dfrac{8}{4}-\left|x-\dfrac{1}{4}\right|\right|-\dfrac{1}{2}=\dfrac{3}{4}\)
\(\Rightarrow\left[{}\begin{matrix}\left|\dfrac{8}{4}-x+\dfrac{1}{4}\right|-\dfrac{1}{2}=\dfrac{3}{4}\\\left|\dfrac{8}{4}+x-\dfrac{1}{4}\right|-\dfrac{1}{2}=\dfrac{3}{4}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left|\dfrac{9}{4}-x\right|-\dfrac{1}{2}=\dfrac{3}{4}\\\left|\dfrac{7}{4}+x\right|-\dfrac{1}{2}=\dfrac{3}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}\dfrac{9}{4}-x-\dfrac{1}{2}=\dfrac{3}{4}\\x=\dfrac{9}{4}-\dfrac{1}{2}=\dfrac{3}{4}\end{matrix}\right.\\\left[{}\begin{matrix}\dfrac{7}{4}+x-\dfrac{1}{2}=\dfrac{3}{4}\\-\dfrac{7}{4}-x-\dfrac{1}{2}=\dfrac{3}{4}\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=1\\x=\dfrac{7}{2}\end{matrix}\right.\\\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=-3\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{7}{2}\\x=-3\end{matrix}\right.\)
Ở nơi x=9/4-1/2 là x-9/4-1/2 nha
a. -1,5 + 2x = 2,5
<=> 2x = 2,5 + 1,5
<=> 2x = 4
<=> x = 2
b. \(\dfrac{3}{2}\left(x+5\right)-\dfrac{1}{2}=\dfrac{4}{3}\)
<=> \(\dfrac{3}{2}x+\dfrac{15}{2}-\dfrac{1}{2}=\dfrac{4}{3}\)
<=> \(\dfrac{9x}{6}+\dfrac{45}{6}-\dfrac{3}{6}=\dfrac{8}{6}\)
<=> 9x + 45 - 3 = 8
<=> 9x = 8 + 3 - 45
<=> 9x = -34
<=> x = \(\dfrac{-34}{9}\)
\(\text{f(1)=}2.1^2+1=3\)
\(\text{f(-1)=}2.\left(-1\right)^2+1=3\)
\(\text{f(2)=}2.2^2+1=9\)
\(\text{f(0)=}2.0^2+1=1\)
\(\text{f(-3)=}=2.\left(-3\right)^2+1=19\)
27: \(\sqrt{\dfrac{81}{25}}-\dfrac{1}{5}\left(-3+\sqrt{16}\right)^{20}\cdot\left(-2\right)^3\)
\(=\dfrac{9}{5}-\dfrac{1}{5}\cdot\left(-8\right)\)
\(=\dfrac{9}{5}+\dfrac{8}{5}=\dfrac{17}{5}\)
28: \(\sqrt{\sqrt{16}}-\sqrt{\sqrt{81}}=2-3=-1\)
Bài 2:
Gọi số cây 7A,7B,7C,7D lần lượt là \(a,b,c,d\in \mathbb{N^*},cây\)
Áp dụng tc dtsbn:
\(\dfrac{a}{3}=\dfrac{b}{4}=\dfrac{c}{5}=\dfrac{d}{6}=\dfrac{b-a}{4-3}=\dfrac{6}{1}=6\\
\Rightarrow\left\{{}\begin{matrix}a=18\\b=24\\c=30\\d=36\end{matrix}\right.\)
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Bài 3:
Gọi số hs 7A,7B,7C,7D lần lượt là \(a,b,c,d\in \mathbb{N^*},hs\)
Áp dụng tc dtsbn:
\(\dfrac{a}{10}=\dfrac{b}{8}=\dfrac{c}{9}=\dfrac{d}{7}=\dfrac{a-d}{10-7}=\dfrac{12}{3}=4\\ \Rightarrow\left\{{}\begin{matrix}a=40\\b=32\\c=36\\d=28\end{matrix}\right.\)
Bài 4:
Gọi số máy 3 đội theo thứ tự là \(a,b,c\in \mathbb{N^*},máy\)
Áp dụng tc dtsbn:
\(4a=6b=8c\Rightarrow\dfrac{a}{6}=\dfrac{b}{4}=\dfrac{c}{3}=\dfrac{a-b}{6-4}=\dfrac{2}{2}=1\\ \Rightarrow\left\{{}\begin{matrix}a=6\\b=4\\c=3\end{matrix}\right.\)
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