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Ta có:
\(\left|4x\right|-\left|-13,5\right|=\left|2\frac{1}{4}\right|\)
\(\Rightarrow\left|4x\right|=\left|2\frac{1}{4}\right|+\left|-13,5\right|=2\frac{1}{4}+13,5=\frac{63}{4}\)
\(\Rightarrow\left[{}\begin{matrix}4x=\frac{63}{4}\\4x=-\frac{63}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{63}{16}\\x=\frac{-63}{16}\end{matrix}\right.\)
1) |4x|-|-13,5|+|9/4|
=> 4x - 13,5 +9/4
=> 4x- 11,25
=> 4x = 11,25
=> x = 11,25:4 = 2,8125
2) x-24=y => x-y = 24
=> x/7 = y/3 = (x-y)/(7-3) = 24/4 = 6
=> x = 42 ; y=18
pt đã cho \(\Leftrightarrow4\left|x\right|-13,5=2\dfrac{1}{4}\Leftrightarrow4\left|x\right|=2\dfrac{1}{4}+13,5\Leftrightarrow4\left|x\right|=\dfrac{63}{4}\Leftrightarrow\left|x\right|=\dfrac{63}{16}\Leftrightarrow x=\pm\dfrac{63}{16}\)
kl: x= +- 63/16
Giải:
\(\left|4x\right|-\left|-13,5\right|=\left|2\dfrac{1}{4}\right|\)
\(\Leftrightarrow\left|4x\right|-13,5=2\dfrac{1}{4}\)
\(\Leftrightarrow\left|4x\right|-13,5=\dfrac{9}{4}\)
\(\Leftrightarrow\left|4x\right|=\dfrac{9}{4}+13,5\)
\(\Leftrightarrow\left|4x\right|=15,75\)
\(\Leftrightarrow\left[{}\begin{matrix}4x=15,75\\4x=-15,75\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3,9375\\x=-3,9375\end{matrix}\right.\)
Vậy ...
a)\(\left(\frac{1}{3}\right)^{-1}-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^4.2^3=3-1+\frac{1}{16}.8=3-1+\frac{1}{2}=\frac{5}{2}\\ \)
b)\(2^2.2^3.\left(\frac{2}{3}\right)^{-2}=2^5.\frac{9}{4}=72\)
c)\(\left(\frac{4}{3}\right)^{-2}.\left(\frac{3}{4}\right)^3:\left(\frac{-2}{3}\right)^{-3}=\left(\frac{3}{4}\right)^2.\left(\frac{3}{4}\right)^3:\left(\frac{-2}{3}\right)^{-3}=\left(\frac{3}{4}\right)^5:\left(\frac{3}{2}\right)^3=\frac{9}{128}\)
2)
\(3^{x+1}=9^x\Leftrightarrow3^x.3=9^x\Rightarrow3=9^x:3^x\Rightarrow3=3^x\Rightarrow x=1\)
\(\left(x-0,1\right)^2=6,25\Leftrightarrow\left(x-0,1\right)^2=2,5^2\Rightarrow\left(x-0,1\right)=2,5\Rightarrow x=2,5+0,1=2,6\)
\(3^{2x-1}=243\Leftrightarrow3^{2x-1}=3^5\Rightarrow2x-1=5\Rightarrow2x=6\Rightarrow x=3\)
\(\left(4x-3\right)^4=\left(4x-3\right)^2\Rightarrow x=1\)
tự bấm máy ra