Giải pt: (2x-3)(2x+3)=2(2x-3)(2x-3)
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`|2x+1|-3=x+4`
`<=>|2x+1|=x+4+3=x+7(x>=-7)`
`**2x+1=x+7`
`<=>x=7-1=6(tm)`
`**2x+1=-x-7`
`<=>3x=-6`
`<=>x=-2(tm)`
`|3x-5|=1-3x(x<=1/3)`
`**3x-5=1-3x`
`<=>6x=6`
`<=>x=1(l)`
`**3x-5=3x-1`
`<=>-5=-1` vô lý
`|2x+2|+|x-1|=10`
Nếu `x>=1`
`pt<=>2x+2+x-1=10`
`<=>3x+1=10`
`<=>3x=9`
`<=>x=3(tm)`
Nếu `x<=-1`
`pt<=>-2x-2+1-x=10`
`<=>-1-3x=10`
`<=>-11=3x`
`<=>x=-11/3(tm)`
Nếu `-1<=x<=1`
`pt<=>2x+2+1-x=10`
`<=>x+3=10`
`<=>x=7(l)`
Vậy `S={3,-11/3}`
\(\left(\dfrac{1}{3}+\dfrac{1}{6}\right)\cdot2^{x+4}-2^x=2^{13}-2^{10}\)
\(\Rightarrow\dfrac{1}{2}\cdot2^{x+4}-2^x=2^{13}-2^{10}\)
\(\Rightarrow2^{x+3}-2^x=2^{13}-2^{10}\)
\(\Rightarrow x+3=13;x+0=10\)
\(\Rightarrow x=10\)
(\(\dfrac{1}{3}\) +\(\dfrac{1}{6}\) ) . 2x+4 - 2x = 213 - 210
(\(\dfrac{2}{6}\) + \(\dfrac{1}{6}\)) . \(2^{x+4}\) - \(2^x\) = 8192 - 1024
\(\dfrac{3}{6}\) . 2x . \(2^4\) -\(2^x\) = 7168
8 . 2x - 2x . 1 = 7168
2x . ( 8 - 1 ) = 7168
2x . 7 = 7168
2x = 7168 : 7
2x = 1024
2x = \(2^{10}\)
⇒ x = 10
3 mũ 2x .(1+3²)=90
=>3 mũ 2x=9=>3 mũ 2x=3²
=>2x=2=>x=1
\(\left(2x-3\right)\left(2x+3\right)=2\left(2x-3\right)\left(2x-3\right)\)
\(\Leftrightarrow\left(2x-3\right)\left(2x+3\right)-2\left(2x-3\right)\left(2x-3\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(2x+3-4x+6\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(-2x+9\right)=0\)
\(\Leftrightarrow2x-3=0\) hay \(-2x+9=0\)
\(\Leftrightarrow x=\dfrac{3}{2}\) hay \(x=\dfrac{9}{2}\)
-Vậy \(S=\left\{\dfrac{3}{2};\dfrac{9}{2}\right\}\)