Tìm x biết x+3/9 = 2x-5/10.
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`Answer:`
a. \(x^3+6x^2+12=19\)
\(\Leftrightarrow x^3+6x^2+12x-19=0\)
\(\Leftrightarrow x^3-x^2+7x^2-7x+19x-19=0\)
\(\Leftrightarrow x^2.\left(x-1\right)+7x\left(x-1\right)+19\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+7x+19\right)=0\)
Ta có \(x^2+7x+19=x^2+2x.3,5+12,25+6,75=\left(x+3,5\right)^2+6,75>0\)
\(\Rightarrow x-1=0\Leftrightarrow x=1\)
b. \(5\left(x+9\right)^2.\left(x-4\right)^3-10\left(x+9\right)^3.\left(x-4\right)^2=0\)
\(\Leftrightarrow5\left(x+9\right)^2.\left(x-4\right)^2.[x-4-2\left(x+9\right)]=0\)
\(\Leftrightarrow\left(x+9\right)^2.\left(x-4\right)^2.\left(x-4-2x-18\right)=0\)
\(\Leftrightarrow\left(x+9\right)^2.\left(x-4\right)^2.\left(-x-22\right)=0\)
\(\Leftrightarrow\left(x+9\right)^2=0\) hoặc \(\left(x-4\right)^2=0\) hoặc \(-x-22=0\)
\(\Leftrightarrow x+9=0\) hoặc \(x-4=0\) hoặc \(-x=22\)
\(\Leftrightarrow x=-9\) hoặc \(x=4\) hoặc \(x=-22\)
c. \(\left(2x+3\right)^2+\left(x-2\right)^2-2\left(2x+3\right)\left(x-2\right)\)
\(=\left(2x+3\right)^2-2\left(2x+3\right)\left(x-2\right)+\left(x-2\right)^2\)
\(=\left(2x+3-x+2\right)^2\)
\(=\left(x+5\right)^2\)
a) x+2(3-x)-3(1-x)=9
<=> x+6-2x-3+3x=9
<=> 2x+3=9
<=> 2x=6
<=> x=3
b) (3x+5)-(x-10)+2x=31
<=> 3x+5-x+10+2x=31
<=> 4x+15=31
<=> 4x=16
<=> x=4
a) x+2(3-x)-3(1-x)=9
x+6-2x-3+3x=9
x-2x+3x=9-6+3
2x=6
x=6:2
x=3
Vậy x=3
b) (3x+5)-(x-10)+2x=31
3x+5-x+10+2x=31
3x-x+2x=31-5-10
4x=16
x=16:4
x=4
Vậy x=4
a)(x+2).(x+3)-(x-2).(x+5)=10
( x^2 +3x+2x+6)-(x^2 +5x-2x-10)=10
x^2 +3x+2x+6-x^2 -5x+2x+10-10=0
2x+6=0
2x=-6
x=-3
a) 5 + 45(2x - 1) = 10
45(2x - 1) = 10 - 5
45(2x - 1) = 5
2x - 1 = 5 : 45
2x - 1 = 1/9
2x = 1/9 + 1
2x = 10/9
x = 10/9 : 2
x = 5/9
b) 54 : (2ˣ⁻³ + 1) + 3 = 9
54 : (2ˣ⁻³ + 1) = 9 - 3
54 : (2ˣ⁻³ + 1) = 6
2ˣ⁻³ + 1 = 54 : 6
2ˣ⁻³ + 1 = 9
2ˣ⁻³ = 9 - 1
2ˣ⁻³ = 8
2ˣ⁻³ = 2³
x - 3 = 3
x = 3 + 3
x = 6
c) 14 + 36 : 3ˣ⁻⁵ = 18
36 : 3ˣ⁻⁵ = 18 - 14
36 : 3ˣ⁻⁵ = 4
3ˣ⁻⁵ = 36 : 4
3ˣ⁻⁵ = 9
3ˣ⁻⁵ = 3²
x - 5 = 2
x = 2 + 5
x = 7
a: =>45(2x-1)=5
=>2x-1=1/9
=>2x=10/9
=>x=5/9
b: =>\(\dfrac{54}{2^{x-3}+1}=6\)
=>\(2^{x-3}+1=9\)
=>\(2^{x-3}=8\)
=>x-3=3
=>x=6
c: \(14+36:3^{x-5}=18\)
=>\(\dfrac{36}{3^{x-5}}=18-14=4\)
=>\(3^{x-5}=9\)
=>x-5=2
=>x=7
a: \(\Leftrightarrow\left|x-1\right|=3-2x\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-3-x+1\right)\left(2x+3+x-1\right)=0\\x< =\dfrac{3}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(x-2\right)\left(3x+2\right)=0\\x< =\dfrac{3}{2}\end{matrix}\right.\)
=>x=-2/3
b: Trường hợp 1: x<-3
Pt sẽ là:
\(-x-1-x-3=10-4x\)
=>-2x-4=10-4x
=>2x=14
hay x=7(loại)
Trường hợp 2: -3<=x<-1
Pt sẽ là \(x+3-x-1=10-4x\)
=>10-4x=2
=>4x=8
hay x=2(loại)
Trường hợp 3: x>=-1
Pt sẽ là x+1+x+3=10-4x
=>2x+4=10-4x
=>6x=6
hay x=1(nhận)