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\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(\dfrac{1}{3}-\dfrac{5}{4}\right)-\left(\dfrac{2}{7}+\dfrac{1}{3}\right)\right]\right\}\)
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(-\dfrac{11}{12}\right)-\dfrac{13}{21}\right]\right\}\)
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\dfrac{85}{84}\right\}\)
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left(-\dfrac{3}{7}\right)\)
\(B=\dfrac{11}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\dfrac{3}{2}-\dfrac{2}{21}-\dfrac{7}{12}+\left[\dfrac{15}{21}-\dfrac{1}{3}+\dfrac{5}{4}-\dfrac{2}{7}-\dfrac{1}{3}\right]\)
=11/12-2/21+5/7-2/3+5/4-2/7
=11/12-2/3+5/4-2/21+3/7
=11/12-8/12+15/12-2/21+9/21
=18/12+7/21
=3/2+1/3
=9/6+2/6=11/6
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\(\left|\frac{13}{4}-2x\right|=\frac{2}{5}+\frac{5}{2}=\frac{29}{10}\left(1\right)\)
+ Nếu \(\frac{13}{4}-2x\ge0\Leftrightarrow x\le\frac{13}{8}\)
\(\Rightarrow\left(1\right)\Leftrightarrow\frac{13}{4}-2x=\frac{29}{10}\Rightarrow x=\frac{7}{40}\) so với điều kiện \(x\le\frac{13}{8}\) nên thoả mãn
+ Nếu \(\frac{13}{4}-2x< 0\Leftrightarrow x>\frac{13}{8}\)
\(\Rightarrow\left(1\right)\Leftrightarrow2x-\frac{13}{4}=\frac{29}{10}\Leftrightarrow x=\frac{123}{40}\) so với điều kiện \(x>\frac{13}{8}=\frac{65}{40}\) nên thoả mãn
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`@` `\text {Ans}`
`\downarrow`
`a)`
`2^2 * 16 \ge 2^x \ge 4^2`
`=> 2^2 * 2^4 \ge 2^x \ge 2^4`
`=> 2^6 \ge 2^x \ge 2^4`
`=> x \in {4; 5; 6}`
`b)`
`9*27 \le 3^x \le 243`
`=> 3^2 * 3^3 \le 3^x \le 3^5`
`=> 3^5 \le 3^x \le 3^5`
`=> x = 5`
`c)`
`2 * (x - 1/2)^2 - 1/8 = 0`
`=> 2* (x - 1/2)^2 = 1/8`
`=> (x - 1/2)^2 = 1/8 \div 2`
`=> (x-1/2)^2 = 1/16`
`=> (x - 1/2)^2 = (+- 1/4)^2`
`=>`\(\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{1}{4}\\x-\dfrac{1}{2}=-\dfrac{1}{4}\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=\dfrac{1}{4}+\dfrac{1}{2}\\x=\dfrac{1}{2}-\dfrac{1}{4}\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=\dfrac{1}{4}\end{matrix}\right.\)
Vậy, `x \in {1/4; 3/4}.`
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4/ Vì 4x/6y=2x+8/3y+11
\(\Rightarrow\) 4x(3y+11)=6y(2x+8)
\(\Rightarrow\) 12xy+44xy= 12xy+48xy
\(\Rightarrow\) 44xy= 48xy
\(\Rightarrow\frac{x}{y}=\frac{48}{44}=\frac{12}{11}\)
A = (\(\dfrac{3}{2}\)- \(\dfrac{1}{4}\))\(^2\) : 12014 + (-\(\dfrac{1}{2}\))2 x \(\dfrac{4}{3}\)
A =\((\)\(\dfrac{5}{4}\))2 + \(\dfrac{1}{4}\)x \(\dfrac{4}{3}\)
A = \(\dfrac{25}{16}\) + \(\dfrac{1}{3}\)
A = \(\dfrac{91}{48}\)