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1) (x+6)(3x-1)+x+6=0
⇔(x+6)(3x-1)+(x+6)=0
⇔(x+6)(3x-1+1)=0
⇔3x(x+6)=0
2) (x+4)(5x+9)-x-4=0
⇔(x+4)(5x+9)-(x+4)=0
⇔(x+4)(5x+9-1)=0
⇔(x+4)(5x+8)=0
3)(1-x)(5x+3)÷(3x-7)(x-1)
=\(\frac{\left(1-x\right)\left(5x+3\right)}{\left(3x-7\right)\left(x-1\right)}=\frac{\left(1-x\right)\left(5x+3\right)}{\left(7-3x\right)\left(1-x\right)}=\frac{\left(5x+3\right)}{\left(7-3x\right)}\)
Tìm x:
1. 3x (2x + 3) - (2x + 5).(3x - 2) = 8
\(\Leftrightarrow6x^2+9x-6x^2+4x-15x+10=0 \)
\(\Leftrightarrow-2x+10=0\Leftrightarrow x=5\)
Vậy x = 5
2. 4x (x -1) - 3(x2 - 5) -x2 = (x - 3) - (x + 4)
\(\Leftrightarrow4x^2-4x-3x^2+15-x^2=x-3-x-4\)
\(\Leftrightarrow-4x+15=-7\)
\(\Leftrightarrow-4x=-22\Leftrightarrow x=\frac{11}{2}\)
Vậy x = \(\frac{11}{2}\)
3. 2 (3x -1) (2x +5) - 6 (2x - 1) (x + 2) = -6
\(\Leftrightarrow2\left(6x^2+15x-2x-5\right)-6\left(2x^2+4x-x-2\right)=-6\)
\(\Leftrightarrow12x^2+30x-4x-10-12x^2-24x+6x+12=-6\)
\(\Leftrightarrow8x=-8\Leftrightarrow x=-1\)
Vậy x = -1
4. 3 ( 2x - 1) (3x - 1) - (2x - 3) (9x - 1) - 3 = -3
\(\Leftrightarrow3\left(6x^2-2x-3x+1\right)-18x^2+2x+27x-3-3=-3\)
\(\Leftrightarrow18x^2-6x-9x+3-18x^2+2x+27x-6=-3\)
\(\Leftrightarrow14x=0\Leftrightarrow x=0\)
Vậy x = 0
5. (3x - 1) (2x + 7) - ( x + 1) (6x - 5) = (x + 2) - (x - 5)
\(\Leftrightarrow6x^2+21x-2x-7-6x^2+5x-6x+5=7\)
\(\Leftrightarrow18x=9\Leftrightarrow x=\frac{1}{2}\)
Vậy x = \(\frac{1}{2}\)
6. 3xy (x + y) - (x + y) (x2 + y2 + 2xy) + y3 = 27
\(\Leftrightarrow3x^2y+3xy^2-\left(x+y\right)^3+y^3=27\)
\(\Leftrightarrow3x^2y+3xy^2-x^3-y^3-3x^2y-3xy^2+y^3=27\)
\(\Leftrightarrow-x^3=27\)
\(\Leftrightarrow x=-3\)
Vậy x = -3
7. 3x (8x - 4) - 6x (4x - 3) = 30
\(\Leftrightarrow24x^2-12x-24x^2+12x=30\)
\(\Leftrightarrow0=30\) ( vô lý)
Vậy pt vô nghiệm
8. 3x (5 - 2x) + 2x (3x - 5) = 20
\(\Leftrightarrow15x-6x^2+6x^2-10x=20\)
\(\Leftrightarrow5x=20\Leftrightarrow x=4\)
Vậy x = 4
Bài 1:
1. \(x-8=3-2\left(x+4\right)\)
\(x-8=3-2x-8\)
\(3x=3\Rightarrow x=1\)
2. \(2\left(x+3\right)-3\left(x-1\right)=2\)
\(2x+6-3x+3=2\)
\(-x+9=2\Rightarrow x=7\)
3. \(4\left(x-5\right)-\left(3x-1\right)=x-19\)
\(4x-20-3x+1=x-19\)
\(0x=0\Rightarrow x=0\)
4. \(7-\left(x-2\right)=5\left(2x-3\right)\)
\(7-x+2=10x-15\)
\(-11x=-24\Rightarrow x=\frac{24}{11}\)
5. \(32-4\left(0,5y-5\right)=3y+2\)
\(32-2y+20=3y+2\)
\(-5y=-50\Rightarrow y=10\)
6. \(3\left(x-1\right)-x=2x-3\)
\(3x-3-x=2x-3\)
\(0x=0\Rightarrow x=0\)
Bài 2:
1. \(\frac{2-x}{3}=\frac{3-2x}{5}\)
\(\frac{\left(2-x\right)5}{15}-\frac{\left(3-2x\right)3}{15}=0\)
\(\frac{10-5x-9+6x}{15}=0\)
\(x+1=0\Rightarrow x=-1\)
2. \(\frac{3-4x}{4}=\frac{x+2}{5}\)
\(\frac{5\left(3-4x\right)}{20}-\frac{4\left(x+2\right)}{20}=0\)
\(\frac{15-20x-4x-8}{20}=0\)
\(7-24x=0\)
\(24x=7\Rightarrow x=\frac{7}{24}\)
a) \(3\left(x^2-2x+1\right)+x\left(2-3x\right)=7\)
\(\Rightarrow3x^2-6x+3+2x-3x^2=7\)
\(\Rightarrow-4x+3=7\)
\(\Rightarrow-4x+3-7=0\)
\(\Rightarrow-4x-4=0\)
\(\Rightarrow-4\left(x+1\right)=0\)
\(\Rightarrow x+1=0\)
\(\Rightarrow x=-1\)
b) \(5\left(x-2\right)+2\left(x+3\right)=10\)
\(\Rightarrow5x-10+2x+6=10\)
\(\Rightarrow7x-4=10\)
\(\Rightarrow7x=10+4=14\)
\(\Rightarrow x=\dfrac{14}{7}=2\)
c) \(\left(x+1\right)\left(-3\right)+5\left(x-4\right)=-3\)
\(\Rightarrow-3x-3+5x-20=-3\)
\(\Rightarrow2x-23=-3\)
\(\Rightarrow2x=-3+23=20\)
\(\Rightarrow x=\dfrac{20}{2}=10\)
d) \(2\left(x-1\right)-x\left(3-x\right)=x^2\)
\(\Rightarrow2x-2-3x+x^2=x^2\)
\(\Rightarrow-x-2+x^2-x^2=0\)
\(\Rightarrow-x-2=0\)
\(\Rightarrow-x=2\)
\(\Rightarrow x=-2\)
đ) \(3x\left(x+5\right)-2\left(x+5\right)=3x^2\)
\(\Rightarrow3x^2+15x-2x-10=3x^2\)
\(\Rightarrow3x^2-3x^2+13x-10=0\)
\(\Rightarrow13x-10=0\)
\(\Rightarrow13x=10\)
\(\Rightarrow x=\dfrac{10}{13}\)
e) \(4x\left(x+2\right)+x\left(4-x\right)=3x^2+12\)
\(\Rightarrow4x^2+8x+4x-x^2=3x^2+12\)
\(\Rightarrow3x^2+12x=3x^2+12\)
\(\Rightarrow3x^2+12x-3x^2-12=0\)
\(\Rightarrow12\left(x-1\right)=0\)
\(\Rightarrow x-1=0\)
\(\Rightarrow x=1\)
f) \(\dfrac{1}{3}x\left(3x+6\right)-x\left(x-5\right)=9\)
\(\Rightarrow x^2+2x-x^2+5x=9\)
\(\Rightarrow7x=9\)
\(\Rightarrow x=\dfrac{9}{7}\)
(x+2)(x+3)-(x-2)(x+5)=0
=> x2+5x+6-x2-3x+10=0
=>2x+16=0
=>2x=-16
=>x=-8
1, x+3(x-1)=4 => 4x-3=4 => 4x=7 => x=\(\dfrac{7}{4}\)
2, 2.(x-3)+5=3 => 2x-6+5=3 =>2x=4 => x=2
3, x.(x-2)-\(x^2\)=-2 => \(x^2-2x-x^2\)=-2 => -2x=-2 => x=1
4, \(x^2-x.\left(x+2\right)=6\)=> \(x^2-x^2-2x=6\)=> -2x=6 => x=-3
5,3x.(x-5)-3x.(x-3)=6 => \(3x^2-15x-3x^2+9x=6\) => -6x=6 => x=-1
6, 3.(\(x^2-2x+1\))+x.(2-3x)=7 => \(3x^2-6x+3+2x-3x^2=7\)=> -4x=4=> x=-1