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a,\(2\left(3x-1\right)-5\left(x-3\right)-9\left(2x-4\right)=24\)
\(< =>6x-2-5x+15-18x+36=24\)
\(< =>-29x+49=24< =>29x=25< =>x=\frac{25}{29}\)
b,\(2x^2+4\left(x^2-1\right)=2x\left(3x+1\right)\)
\(< =>2x^2+4x^2-4=6x^2+2x\)
\(< =>2x=-4< =>x=-\frac{4}{2}=-2\)
c, \(2x\left(5-3x\right)+2x\left(3x-5\right)-3\left(x-7\right)=4\)
\(< =>10x-6x^2+6x^2-10x-3x+21=4\)
\(< =>-3x=4-21=-17< =>x=\frac{17}{3}\)
d, \(5x\left(x+1\right)-4x\left(x+2\right)=1-x\)
\(< =>5x^2+5x-4x^2-8x=1-x\)
\(< =>x^2-3x+x-1=0\)
\(< =>x^2-2x-1=0\)
\(< =>\left(x-1\right)^2=2\)
\(< =>\orbr{\begin{cases}x-1=\sqrt{2}\\x-1=-\sqrt{2}\end{cases}}\)
\(< =>\orbr{\begin{cases}x=1+\sqrt{2}\\x=1-\sqrt{2}\end{cases}}\)
a) \(x^3+3x^2+3x+2=0\)
<=> \(x^3+x^2+x+2x^2+2x+2=0\)
<=> \(x\left(x^2+x+1\right)+2\left(x^2+x+1\right)=0\)
<=> \(\left(x+2\right)\left(x^2+x+1\right)=0\)
tự làm
b) \(x^4-2x^3+2x-1=0\)
<=> \(\left(x^4-3x^3+3x^2-x\right)+\left(x^3-3x^2+3x-1\right)=0\)
<=> \(x\left(x^3-3x^2+3x-1\right)+\left(x^3-3x^2+3x-1\right)=0\)
<=> \(\left(x^3-3x^2+3x-1\right)\left(x+1\right)=0\)
<=> \(\left(x-1\right)^3\left(x+1\right)=0\)
tự làm
c) \(x^4-3x^3-6x^2+8x=0\)
<=> \(x\left(x^3-3x^2-6x+8\right)=0\)
<=> \(x\left[\left(x^3+x^2-2x\right)-\left(4x^2+4x-8\right)\right]=0\)
<=>\(x\left[x\left(x^2+x-2\right)-4\left(x^2+x-2\right)\right]=0\)
<=> \(x\left(x-4\right)\left(x^2+x-2\right)=0\)
<=> \(x\left(x-4\right)\left(x-1\right)\left(x+2\right)=0\)
tự làm
a) \(3x\left(2x+3\right)-\left(2x+5x\right)\left(3x-2\right)=8\)
\(\Leftrightarrow6x^2+9x-\left(6x^2-4x+15x^2-10x\right)=8\)
\(\Leftrightarrow6x^2+9x-6x^2+4x-15x^2+10x=8\)
\(\Leftrightarrow23x-15x^2-8=0\)
\(\Leftrightarrow-15x\left(x-1\right)+8\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(8-15x\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\8-15x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=\frac{8}{15}\end{cases}}}\)
Vậy ....
\(3x\left(2x+3\right)-\left(2x+5x\right)\left(3x-2\right)=8\)
\(\Leftrightarrow6x^2+9x-\left(6x^2-4x+15x^2-10x\right)=8\)
\(\Leftrightarrow6x^2+9x-6x^2+4x-15x^2+10x=8\)
\(\Leftrightarrow-15x^2+23x-8=0\)
\(\Leftrightarrow-\left(15x^2-23x+8\right)=0\)
\(\Leftrightarrow-\left(15x^2-15x-8x+8\right)=0\)
\(\Leftrightarrow-\left(15x-8\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left(1-x\right)\left(15x-8\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}1-x=0\\15x-8=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=\frac{8}{15}\end{cases}}}\)
\(a,5\left(3x+5\right)-4\left(2x-3\right)=5x+8\left(2x+12\right)+1\)
\(\Rightarrow5\left(3x+5\right)-4\left(2x-3\right)-5x-8\left(2x+12\right)-1=0\)
\(\Rightarrow15x+25-8x+12-5x-16x-96-1=0\)
\(\Rightarrow-14x-60=0\)
\(\Rightarrow-14x=60\) \(\Rightarrow x=-\frac{60}{14}=\frac{-30}{7}\)
\(b,\left(2x+3\right)\left(x-4\right)-\left(3x-5\right)\left(x-4\right)=\left(5-x\right)\left(x-2\right)\)
\(\Rightarrow2x^2+3x-8x-12-3x^2+5x+12x-20=5x-x^2-10+2x\)
\(\Rightarrow-x^2+12x-32=7x-x^2-10\)
\(\Rightarrow-x^2+12x-32-7x+x^2+10=0\)
\(\Rightarrow5x-22=0\)
\(\Rightarrow5x=22\Rightarrow x=\frac{22}{5}\)
a) 5(3x+5)-4(2x-3) = 5x+8(2x+12)+1
15x + 25 - 8x + 12 = 5x + 16x + 96 + 1
15x - 8x - 5x - 16x = 96 + 1 - 25 - 12
-14x = 60
x = \(\frac{60}{-14}\)
x = \(-\frac{30}{7}\)
b) (2x+3)(x-4)-(3x-5)(x-4) = (5-x).(x-2)
(x - 4)(2x + 3 - 3x +5) = 5x - 10 - x2 + 2x
(x - 4)[(2x - 3x) + (3 + 5)] = 5x - 10 - x2 + 2x
(x - 4)(-x + 8) = 5x - 10 - x2 + 2x
-x2 + 8x + 4x - 32 = 5x - 10 - x2 + 2x
(-x2 + x2) + (8x + 4x - 5x - 2x) = -10 + 32
5x = 22
x = \(\frac{22}{5}\)
a, ( 3x - 1 )^2 - 3x( 3x + 2 ) = 0
<=>9x2-6x+1-9x2-6x=0
<=>-12x+1=0
<=>-12x=-1
<=>x=1/12
b, ( 2x + 3)^2 = 4x(x + 1 )
<=>(2x+3)2-4x(x+1)=0
<=>4x2+12x+9-4x2-4x=0
<=>8x+9=0
<=>8x=-9
<=>x=-9/8
c) vô fx gõ lại
d)x2-4x+4=16
<=>(x-2)2-16=0
<=>(x-2)2-42=0
<=>(x-2+4)(x-2-4)=0
<=>(x+2)(x-6)=0
<=>x+2=0 hoặc x-6=0
<=>x=-2 hoặc x=6
a)4×(x-5)-(x-1)×(4x-3)=5
=>4x-20-4x2+7x-3-5=0
=>-4x2+11x-28=0
=>-4(x2-\(\frac{11x}{4}\)+7)=0
=>\(-4\left(x-\frac{11}{8}\right)^2-\frac{327}{16}< 0\)
=>vô nghiệm
b) (3x-4)(x-2)=3x(x-9)-3
=>3x2-10x+8=3x2-27x-3
=>17x=-11
=>x=-11/17
c)(x-5)×(x-4)-(x+1)×(x-2)=7
=>x2-9x+20-x2+x+2=7
=>22-8x=7
=>-8x=-15
=>x=8/15