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a) \(5^{x+1}-2.5^x=375\)
\(\Rightarrow5^x\left(5-2\right)=375\)
\(\Rightarrow5^x.3=375\)
\(\Rightarrow5^x=125=5^3\)
\(\Rightarrow x=3\)
b) \(9^{x+1}-5.3^{2x}=324\)
\(\Rightarrow3^{2\left(x+1\right)}-5.3^{2x}=324\)
\(\Rightarrow3^2\left(3^{x+1}-5.3^x\right)=324\)
\(\Rightarrow9.3^x\left(3-5\right)=324\)
\(\Rightarrow3^x.\left(-2\right)=36\)
\(\Rightarrow3^x=-18=3^2.\left(-2\right)\)(vô lí vì 3x không chia hết cho 2)
c) \(\left(1-x\right)^5=32=2^5\)
\(\Rightarrow1-x=2\)
\(\Rightarrow x=-1\)
d) \(3.5^{2x+1}-3.25^x=300\)
\(\Rightarrow3\left(5^{2x}.5-5^{2x}\right)=300\)
\(\Rightarrow5^{2x}\left(5-1\right)=100\)
\(\Rightarrow5^{2x}.4=100\)
\(\Rightarrow5^{2x}=25=5^2\)
\(\Rightarrow2x=2\)
\(\Rightarrow x=1\)
A(x) + B(x) = 2x3 - 6x
2x3 - 6x = 0 => x= 0 và x = căn 3 và x = - căn 3
\(\frac{x+2}{x-1}=\frac{x-3}{x+1}\Leftrightarrow\left(x+2\right)\left(x+1\right)=\left(x-1\right)\left(x-3\right)\Leftrightarrow x^2+3x+2=x^2-4x+3\)
\(\Leftrightarrow x^2+3x+2-x^2+4x-3=0\Leftrightarrow7x-1=0\Leftrightarrow7x=1\Leftrightarrow x=\frac{1}{7}\)
=>(x+2)(x+1)=(x-1)(x-3)
x.x+x.1+2x+2.1=x.x-3x-1x+1.3
x2+x+2x+2=x2-3x-1x+3
x2+(x+2x)+2=x2+(-3x-1x)+3
x2+3x+2=x2-4x+3
x2+3x-x2+4x=3-2
(x2-x2)+(3x+4x)=1
7x=1
x=1/7
a)|x|-x=3/4 =>.x-x=3/4=>0x=3/4 ( vo li)
hoac-x-x=3/4=>-2x=3/4=>x=3/4:(-2)=-3/8
b)|x-2|=x =>x-2=x=>0x=2(vo li)
hoac x-2=-x=>2x=2=>x=1
c)giai tuonh tu cau b nhe
\(TH1:a,2\left|x-3\right|+\left|2x+5\right|=11\)
\(\Rightarrow2x-6+2x+5=11\)
\(\Rightarrow4x-1=11\)
\(\Rightarrow4x=12\)
\(\Rightarrow x=3\)
\(TH2:2\left|x-3\right|+\left|2x+5\right|=11\)
\(\Rightarrow-2x+6-2x-5=11\)
\(\Rightarrow-4x+1=11\)
\(\Rightarrow-4x=10\)
\(\Rightarrow x=-2,5\)
\(TH1:b,\left|x-3\right|+\left|5-x\right|+2\left|x-4\right|=2.2\)
\(\Rightarrow x-3+5-x+2x-8=4\)
\(\Rightarrow2x-6=4\)
\(\Rightarrow x=5\)
\(TH2:\left|x-3\right|+\left|5-x\right|+2\left|x-4\right|=4\)
\(\Rightarrow-x+3-5+x-2x+8=4\)
\(\Rightarrow-2x+6=4\)
\(\Rightarrow x=1\)
Vì \(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+...+\left|x+9\right|\ge0.Với\forall x\in I\)
\(\Rightarrow14x\ge0\Leftrightarrow x\ge0\)
\(\Rightarrow x+1+x+2+x+3+...+x+9=14x\)
\(\Rightarrow9x+55=14x\)
\(\Rightarrow55=5x\)
\(\Rightarrow x=11\)