2x + 3x = 10
giúp mk nha
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Lời giải:
$3^{n+2}-2^{n+2}+3^n-2^n=9.3^n-4.2^n+3^n-2^n$
$=(9.3^n+3^n)-(4.2^n+2^n)=10.3^n-5.2^n$
$=10.3^n-10.2^{n-1}=10(3^n-2^{n-1})\vdots 10$ với mọi $n\in\mathbb{N}^*$
`|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}`
a) \(A=\left(2x-1\right)\left(x+3\right)-\left(x-2\right)\left(3x-4\right)+5x\)
\(=\left(2x^2+6x-x-3\right)-\left(3x^2-4x-6x+8\right)+5x\)
\(=\left(2x^2+5x-3\right)-\left(3x^2-10x+8\right)+5x\)
\(=2x^2+5x-3-3x^2+10x-8+5x\)
\(=x^2+20x-11\)
b) \(5x\left(2x^2-3x+1\right)-2x\left(x+1\right)\left(x-2\right)\)
\(=10x^3-15x^2+5x-2x\left(x^2-2x+x-2\right)\)
\(=10x^3-15x^2+5x-2x^3+4x^2-2x^2+4x\)
\(=8x^3-13x^2+9x\)
c) \(\left(3x+2\right)\left(x+1\right)-2x\left(x+3\right)-2x+1\)
\(=3x^2+3x+2x+2-2x^2-6x-2x+1\)
\(=x^2-3x+3\)
a, 3x(2x+1)+4<2x(3x-1)-6
\(\Leftrightarrow\)6x2+3x+4<6x2-2x-6
\(\Leftrightarrow\)6x2+3x-6x2+2x < -6-4
\(\Leftrightarrow\)5x<-10
\(\Leftrightarrow\)x<-2
Vậy bpt có nghiệm x<-2
b,(2x-3)2 < (2x+5)(2x-5)
\(\Leftrightarrow\)4x2-6x+9 < 4x2-25
\(\Leftrightarrow\)4x2-6x-4x2 < -25-9
\(\Leftrightarrow\)-6x < -34
\(\Leftrightarrow\)x > \(\frac{17}{3}\)
Vậy bpt có nghiệm x > \(\frac{17}{3}\)
\(\left|2x-1\right|-3=11\)
=> \(\left|2x-1\right|=11+3\)
=> \(\left|2x-1\right|=14\)
=> \(\orbr{\begin{cases}2x-1=14\\2x-1=-14\end{cases}}\)
=> \(\orbr{\begin{cases}2x=15\\2x=-13\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{15}{2}\\x=-\frac{13}{2}\end{cases}}\)
\(\left|-2x+3\right|-3=x\)
=> \(\left|-2x+3\right|=x+3\) (Đk: \(x+3\ge0\) => \(x\ge-3\))
=> \(\orbr{\begin{cases}-2x+3=x+3\\-2x+3=-x-3\end{cases}}\)
=> \(\orbr{\begin{cases}-3x=0\\-x=-6\end{cases}}\)
=> \(\orbr{\begin{cases}x=0\\x=6\end{cases}}\) (tm)
\(2x+3x=10\)
\(\left(2+3\right)\cdot x=10\)
\(5x=10\)
\(x=10:5\)
\(x=2\)
Học tốt nhé bạn
2x+3x=10
5x=10
x=2