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a: \(\Leftrightarrow9x^2-9x+2=9x^2+6x+1\)
=>-3x=-1
hay x=1/3
b: \(\Leftrightarrow4x^2+4x-x-1=4x^2-12x+9\)
=>3x-1=-12x+9
=>15x=10
hay x=2/3
c: \(\Leftrightarrow25x^2+10x+1=25x^2+25x-x-1=24x-1\)
=>10x-24x=-1-1
=>-14x=-2
hay x=1/7
d: \(\Leftrightarrow49x^2-28x+4=49x^2+14x-21x-6\)
=>-28x+4=-7x-6
=>-21x=-10
hay x=10/21
a. \(\left(3x-2\right)\left(3x-1\right)=\left(3x+1\right)^2\)
\(\Leftrightarrow9x^2-9x+2=9x^2+6x+1\)
\(\Leftrightarrow-3x=-1\)
\(\Leftrightarrow x=3\)
\(a,\left(3x-2\right)\left(3x-1\right)=\left(3x+1\right)^2\)
\(9x^2-3x-6x+2=9x^2+6x+1\)
\(-9x+2-6x-1=0\)
\(-15x+1=0\)
\(-15x=-1\)
\(x=\frac{1}{15}\)
a: \(\Leftrightarrow\left(3x+2\right)\left(5-x\right)=-9x^2+4\)
\(\Leftrightarrow\left(3x+2\right)\left(5-x\right)+\left(3x+2\right)\left(3x-2\right)=0\)
\(\Leftrightarrow\left(3x+2\right)\left(2x+3\right)=0\)
=>x=-2/3 hoặc x=-3/2
b: \(\Leftrightarrow4x\left(x+5\right)+x^2-25=0\)
\(\Leftrightarrow\left(x+5\right)\left(5x-5\right)=0\)
=>x=-5 hoặc x=1
c: \(\Leftrightarrow3x\left(x-1\right)=\left(x-1\right)^2\)
\(\Leftrightarrow\left(x-1\right)\left(2x+1\right)=0\)
=>x=1 hoặc x=-1/2
`a,4x-10=0 `
`<=> 4x=10`
`<=>x=10/4`
`<=>x=5/2`
`b, 7-3x=9-x `
`<=>-3x+x=9-7`
`<=>-2x=2`
`<=>x=-1`
`c, 2x-(3-5x) = 4(x+3)`
`<=>2x-3+5x=4x+12`
`<=>2x+5x-4x=12+3`
`<=>3x=15`
`<=>x=5`
`d, 5-(6-x)=4(3-2x) `
`<=>5-6+x=12-8x`
`<=>x+8x=12-5+6`
`<=>9x=13`
`<=>x=13/9`
`e, 4(x+3)=-7x+17 `
`<=>4x+12=-7x+17`
`<=>4x+7x=17-12`
`<=>11x=5`
`<=>x=5/11`
`f, 5(x-3) - 4=2(x-1)+7`
`<=>5x-15-4=2x-2+7`
`<=>5x-2x=15+4-2+7`
`<=>3x=24`
`<=>x=8`
`g, 5(x-3)-4=2(x-1)+7 `
`<=>5x-15-4=2x-2+7`
`<=>5x-2x=15+4-2+7`
`<=>3x=24`
`<=>x=8`
`h,4(3x-2)-3(x-4)=7x+20`
`<=>12x-8-3x+12=7x+20`
`<=>12x-3x-7x=20+8+12`
`<=>2x=40`
`<=>x=20`
\(a. 2x(3x^2-5x+3) = 6x^3-10x^2+6x \)
\(b. -2x(x^2+5x-3) = -2x^3-10x^2+6x\)
c. \(-\dfrac{1}{2}x^2\left(2x^3-4x+3\right)
=-x^5+2x^3-\dfrac{3}{2}x^2\)
\(d.\left(2x-1\right)\left(x^2+5-4\right)=\left(2x-1\right)\left(x^2+1\right)=2x^3+2x-x^2-1\)
e. \(-\left(5x-4\right)\left(2x+3\right)=10x^2+15x-8x-12=-10x^2+7x-12\)
f.\(\left(2x-y\right)\left(4x^2-2xy+y^2\right)=\left(2x-y\right)\left(2x-y\right)^2=\left(2x-y\right)^3\)
g.\(\left(3x-4\right)\left(x+4\right)+\left(5-x\right)\left(2x^2+3x-1\right)=3x^2+12x-4x-16+10x^2+15x-5-2x^3-3x^2+x=-2x^3+10x^2+24x-21\)
e. \(7x\left(x-4\right)-\left(7x+3\right)\left(2x^2-x+4\right)=7x^2-28x-14x^3+7x^2-28x-6x^2+3x+-12=-14x^3+8x^2-53x-12\)
a) \(\left(3x-2\right)\left(3x-1\right)=\left(3x+1\right)^2\)
<=> \(9x^2-9x+2=9x^2+6x+1\)
<=> \(15x=1\) <=> \(x=\frac{1}{15}\)
b) \(\left(4x-1\right)\left(x+1\right)=\left(2x-3\right)^2\)
<=> \(4x^2+3x-1=4x^2-12x+9\)
<=> \(15x^2=10\) <=> \(x=\frac{2}{3}\)
c) \(\left(5x+1\right)^2=\left(7x-3\right)\left(7x+2\right)\) <=> \(25x^2+10x+1=49x^2-7x-6\)
<=> \(24x^2-17x-7=0\) <=> \(24x^2-24x+7x-7=0\)
<=> \(\left(24x+7\right)\left(x-1\right)=0\) <=> \(\orbr{\begin{cases}x=-\frac{7}{24}\\x=1\end{cases}}\)
d) (4 - 3x)(4 + 3x) = (9x - 3)(1 - x)
<=> 16 - 9x2 = 12x - 9x2 - 3
<=> 12x = 19
<=> x = 19/12
e) x(x + 1)(x + 2)(x + 3) = 24
<=> (x2 + 3x)(x2 + 3x + 2) = 24
<=> (x2 + 3x)2 + 2(x2 + 3x) - 24 = 0
<=> (x2 + 3x)2 + 6(x2 + 3x) - 4(x2 + 3x) - 24 = 0
<=> (x2 + 3x + 6)(x2 + 3x - 4) = 0
<=> \(\orbr{\begin{cases}x^2+3x+6=0\\x^2+3x-4=0\end{cases}}\)
<=> \(\orbr{\begin{cases}\left(x+\frac{3}{2}\right)^2+\frac{15}{4}=0\left(vn\right)\\\left(x+4\right)\left(x-1\right)=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=-4\\x=1\end{cases}}\)
g) (7x - 2)2 = (7x - 3)(7x + 2)
<=> 49x2 - 28x + 4 = 49x2 - 7x - 6
<=> 21x = 10 <=> x = 10/21