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\(1-\frac{303030}{313131}+\frac{616161}{626262}-1+\frac{929292}{939393}-1=\left(1-\frac{30}{31}\right)+\left(\frac{61}{62}-1\right)+\left(\frac{92}{93}-1\right)\)
\(=\frac{1}{31}-\frac{1}{62}-\frac{1}{93}=\frac{1}{186}\)
=> \(\frac{\left|x\right|}{186}=\frac{1}{186}\)=> |x| = 1 => x = 1 hoặc x = - 1
Vậy...............
\(\frac{\left|x\right|}{186}=\left(1-\frac{303030}{313131}\right)+\left(\frac{616161}{626262}-1\right)+\left(\frac{929291}{939393}-1\right)\)
<=> \(\frac{\left|x\right|}{186}=-\frac{303030}{313131}+\frac{616161}{626262}+\frac{929292}{939393}+1-1-1\)
<=> \(\frac{\left|x\right|}{186}=-\frac{30}{31}+\frac{61}{62}+\frac{92}{93}+1-1-1\)
<=> \(\frac{\left|x\right|}{186}=\frac{61}{62}+\frac{92}{93}-1-\frac{30}{31}\)
<=> \(\frac{\left|x\right|}{186}=-\frac{1.31}{31}+\frac{61}{62}+\frac{92}{91}-\frac{30}{31}\)
Lấy MSC là 168, ta có:
<=> \(\frac{\left|x\right|}{186}=\frac{-186}{186}+\frac{183}{186}+\frac{184}{186}-\frac{180}{186}\)
<=> \(\frac{\left|x\right|}{186}=\frac{-186+183+184-180}{186}\)
<=> \(\frac{\left|x\right|}{186}=\frac{1}{186}\)
<=> |x| = 1
<=> \(\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)
=> \(\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)
Giá trị của x thỏa mãn:
\(\left(\frac{1}{2}\right)^{x+4}=\left(\frac{1}{4}\right)^{\frac{3}{2}.x-4}\)
\(\left(\frac{1}{2}\right)^{x+4}=\left(\frac{1}{4}\right)^{\frac{3}{2}x-4}\)
=> \(\left(\frac{1}{2}\right)^{x+4}=\left(\frac{1}{2}\right)^{2\left(\frac{3}{2}x-4\right)}\)
=> \(\left(\frac{1}{2}\right)^{x+4}=\left(\frac{1}{2}\right)^{3x-8}\)
=> \(x+4=3x-8\)
=> \(3x-8-x=4\)
=> \(2x-8=4\)
=> \(2x=12\)
=> \(x=\frac{12}{2}=6\)
\(\left(\frac{1}{2}\right)^{-x+4}=\left(\frac{1}{4}\right)^{\frac{3}{2}x-4}\)
=>\(\left(\frac{1}{2}\right)^{-x+4}=\left(\frac{1}{2}\right)^{3x-8}\)
=>-x+4=3x-8
<=>4x=12
<=>x=3
Vậy x=3
\(\left(\frac{1}{4}\right)^{\frac{3}{2}-4}=\left(\frac{1}{2}\right)^{2.\left(\frac{3}{2}-4\right)}=\left(\frac{1}{2}\right)^{-1}\)
; do đó -x + 4 = -1
=> -x = -1 - 4 = -5
=> x = 5
\(\pm3\)
\(\frac{|x|}{186}=\left(1-\frac{30}{31}\right)+\left(\frac{60}{61}-1\right)\)
\(\Leftrightarrow|x|=186\left(\frac{1}{31}-\frac{1}{61}\right)\)
\(\Leftrightarrow|x|=6-\frac{186}{61}\)
\(\Leftrightarrow|x|=\frac{180}{61}\)
\(\Leftrightarrow x=\pm\frac{180}{61}\)