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b)x2-2x+1=4
⇔(x-1)2=4
\(\Leftrightarrow\left[{}\begin{matrix}x-1=2\\x-1=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
c)x2-4x+4=9
⇔ (x-2)2=9
\(\Leftrightarrow\left[{}\begin{matrix}x-2=3\\x-2=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)
d)4x2-4x+1=4
⇔ (2x-1)2=4
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=4\\2x-1=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{-3}{2}\end{matrix}\right.\)
e)x2-2x-8=0
⇔ x2-4x+2x-8=0
⇔ x(x-4)+2(x-4)=0
⇔(x-4)(x+2)=0
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\)
f)9x2-6x-8=0
⇔ 9x2-12x+6x-8=0
⇔ 3x(3x-4)+2(3x-4)=0
⇔ (3x-4)(3x+2)=0
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=\dfrac{-2}{3}\end{matrix}\right.\)
a) \(7x\left(2x-3\right)-\left(4x^2-9\right)=0\Rightarrow7x\left(2x-3\right)-\left(2x-3\right)\left(2x+3\right)=0\Rightarrow\left(2x-3\right)\left(7x-2x+3\right)=0\Rightarrow\left[{}\begin{matrix}2x-3=0\\5x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{3}{5}\end{matrix}\right.\)
b) \(\left(2x-7\right).\left(x-2\right)\left(x^2-4\right)=0\Rightarrow\left(2x-7\right)\left(x-2\right)^2\left(x+2\right)=0\Rightarrow\left[{}\begin{matrix}2x-7=0\\\left(x-2\right)^2=0\\x+2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=2\\x=-2\end{matrix}\right.\)
c)\(\left(9x^2-25\right)-\left(6x-10\right)=0\Rightarrow\left(3x-5\right)\left(3x+5\right)-2\left(3x-5\right)=0\Rightarrow\left(3x-5\right)\left(3x+5-2\right)=0\Rightarrow\left[{}\begin{matrix}3x-5=0\\3x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=1\end{matrix}\right.\)
a: Ta có: \(7x\left(2x-3\right)-\left(4x^2-9\right)=0\)
\(\Leftrightarrow7x\left(2x-3\right)-\left(2x-3\right)\left(2x+3\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(5x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{3}{5}\end{matrix}\right.\)
b: Ta có: \(\left(2x-7\right)\left(x-2\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(2x-7\right)\left(x-2\right)^2\cdot\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=2\\x=-2\end{matrix}\right.\)
c: Ta có: \(\left(9x^2-25\right)-\left(6x-10\right)=0\)
\(\Leftrightarrow\left(3x-5\right)\left(3x+5-2\right)=0\)
\(\Leftrightarrow\left(3x-5\right)\left(3x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=-1\end{matrix}\right.\)
a: \(\Leftrightarrow x\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)
c: \(\Leftrightarrow\left(x-1\right)\left(3x-1\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{3}\\x=-\dfrac{1}{3}\end{matrix}\right.\)
a) \(x^2-6x=0\\ \Leftrightarrow x\left(x-6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)
b) \(\Leftrightarrow\left(3x-1-x-5\right)\left(3x-1+x+5\right)=0\\ \Leftrightarrow\left(2x-6\right)\left(4x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
c) \(9x^2\left(x-1\right)=x-1\\ \Leftrightarrow\left(9x^2-1\right)\left(x-1\right)=0\\ \Leftrightarrow\left(3x-1\right)\left(3x+1\right)\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=-\dfrac{1}{3}\\x=1\end{matrix}\right.\)
d) \(x^2-4=\left(x-2\right)^2\\ \Leftrightarrow\left(x-2\right)\left(x+2-x+2\right)=0\\ \Leftrightarrow4\left(x-2\right)=0\\ \Leftrightarrow x=2\)
e) \(\Leftrightarrow\left(x+3\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-2\end{matrix}\right.\)
f) \(x^3-0,36=0\\ \Leftrightarrow x\left(x^2-0,36\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{3}{5}\\x=\dfrac{3}{5}\end{matrix}\right.\)
g) \(\Leftrightarrow\left(5x-1\right)\left(x-2018\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{5}\\x=2018\end{matrix}\right.\)
h) \(\Leftrightarrow x\left(x-5\right)-4\left(x-5\right)=0\\ \Leftrightarrow\left(x-4\right)\left(x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=4\\x=5\end{matrix}\right.\)
a) x4 - 16x2 = 0
<=> ( x2 )2 - ( 4x )2 = 0
<=> ( x2 - 4x )( x2 + 4x ) = 0
<=> [ x( x - 4 ) ][ x( x + 4 ) ] = 0
<=> x( x - 4 )x( x + 4 ) = 0
<=> x2( x - 4 )( x + 4 ) = 0
<=> \(\hept{\begin{cases}x^2=0\\x-4=0\\x+4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm4\end{cases}}\)( thay bằng dấu hoặc hộ mình nhé )
b) 9x2 + 6x + 1 = 0
<=> ( 3x )2 + 2.3x.1 + 12 = 0
<=> ( 3x + 1 )2 = 0
<=> 3x + 1 = 0
<=> 3x = -1
<=> x = -1/3
c) x2 - 6x = 16
<=> x2 - 6x - 16 = 0
<=> x2 + 2x - 8x - 16 = 0
<=> x( x + 2 ) - 8( x + 2 ) = 0
<=> ( x + 2 )( x - 8 ) = 0
<=> \(\orbr{\begin{cases}x+2=0\\x-8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=8\end{cases}}\)
d) 9x2 + 6x = 80
<=> 9x2 + 6x - 80 = 0
<=> 9x2 + 30x - 24x - 80 = 0
<=> 9x( x + 10/3 ) - 24( x + 10/3 ) = 0
<=> ( x + 10/3 )( 9x - 24 ) = 0
<=> \(\orbr{\begin{cases}x+\frac{10}{3}=0\\9x-24=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{10}{3}\\x=\frac{8}{3}\end{cases}}\)
e) Áp dụng công thức an.bn = ( ab )n ta có :
25( 2x - 1 )2 - 9( x + 1 )2 = 0
<=> 52( 2x - 1 )2 - 32( x + 1 )2 = 0
<=> [ 5( 2x - 1 ) ]2 - [ 3( x + 1 ) ]2 = 0
<=> ( 10x - 5 )2 - ( 3x + 3 )2 = 0
<=> [ ( 10x - 5 ) - ( 3x + 3 ) ][ ( 10x - 5 ) + ( 3x + 3 ) ] = 0
<=> ( 10x - 5 - 3x - 3 )( 10x - 5 + 3x + 3 ) = 0
<=> ( 7x - 8 )( 13x - 2 ) = 0
<=> \(\orbr{\begin{cases}7x-8=0\\13x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{8}{7}\\x=\frac{2}{13}\end{cases}}\)
Bài làm :
a) x4 - 16x2 = 0
<=> ( x2 )2 - ( 4x )2 = 0
<=> ( x2 - 4x )( x2 + 4x ) = 0
<=> [ x( x - 4 ) ][ x( x + 4 ) ] = 0
<=> x( x - 4 )x( x + 4 ) = 0
<=> x2( x - 4 )( x + 4 ) = 0
Vậy x=0 hoặc x=±4
b) 9x2 + 6x + 1 = 0
<=> ( 3x )2 + 2.3x.1 + 12 = 0
<=> ( 3x + 1 )2 = 0
<=> 3x + 1 = 0
<=> 3x = -1
<=> x = -1/3
c) x2 - 6x = 16
<=> x2 - 6x - 16 = 0
<=> x2 + 2x - 8x - 16 = 0
<=> x( x + 2 ) - 8( x + 2 ) = 0
<=> ( x + 2 )( x - 8 ) = 0
\(\Leftrightarrow\orbr{\begin{cases}x+2=0\\x-8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=8\end{cases}}\)
d) 9x2 + 6x = 80
<=> 9x2 + 6x - 80 = 0
<=> 9x2 + 30x - 24x - 80 = 0
<=> 9x( x + 10/3 ) - 24( x + 10/3 ) = 0
<=> ( x + 10/3 )( 9x - 24 ) = 0
\(\Leftrightarrow\orbr{\begin{cases}x+\frac{10}{3}=0\\9x-24=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{10}{3}\\x=\frac{8}{3}\end{cases}}\)
e) 25( 2x - 1 )2 - 9( x + 1 )2 = 0
<=> 52( 2x - 1 )2 - 32( x + 1 )2 = 0
<=> [ 5( 2x - 1 ) ]2 - [ 3( x + 1 ) ]2 = 0
<=> ( 10x - 5 )2 - ( 3x + 3 )2 = 0
<=> [ ( 10x - 5 ) - ( 3x + 3 ) ][ ( 10x - 5 ) + ( 3x + 3 ) ] = 0
<=> ( 10x - 5 - 3x - 3 )( 10x - 5 + 3x + 3 ) = 0
<=> ( 7x - 8 )( 13x - 2 ) = 0
\(\Leftrightarrow\orbr{\begin{cases}7x-8=0\\13x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{8}{7}\\x=\frac{2}{13}\end{cases}}\)
a) Ta có : x4 - 16x2 = 0
=> x4 - 8x2 - 8x2 + 64 = 64
=> x2(x2 - 8) - 8(x2 - 8) = 64
=> (x2 - 8)2 = 64
=> \(\orbr{\begin{cases}x^2-8=8\\x^2-8=-8\end{cases}}\Rightarrow\orbr{\begin{cases}x^2=16\\x^2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\pm4\\x=0\end{cases}}\Rightarrow x\in\left\{4;-4;0\right\}\)
b) Ta có 9x2 + 6x + 1 = 0
=> 9x2 + 3x + 3x + 1 = 0
=> 3x(3x + 1) + (3x + 1) = 0
=> (3x + 1)2 = 0
=> 3x + 1 = 0
=> x = -1/3
c) Ta có x2 - 6x = 16
=> x2 - 6x + 9 = 25
=> (x - 3)2 = 25
=> \(\orbr{\begin{cases}x-3=5\\x-3=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=8\\x=-2\end{cases}}\Rightarrow x\in\left\{8;-2\right\}\)
d) 9x2 + 6x = 80
=> 9x2 + 6x + 1 = 81
=> (3x + 1)2 = 81
=> \(\orbr{\begin{cases}3x+1=9\\3x+1=-9\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{8}{3}\\x=-\frac{10}{3}\end{cases}\Rightarrow x\in}\left\{\frac{8}{3};\frac{-10}{3}\right\}\)
e) 25(2x - 1)2 - 9(x + 1)2 = 0
=> [5(2x - 1)]2 - [3(x + 1)]2 = 0
=> (10x - 5)2 - (3x + 3)2 = 0
=> (10x - 5 - 3x - 3)(10x - 5 + 3x + 3) = 0
=> (7x - 8)(13x - 2) = 0
=> \(\orbr{\begin{cases}7x=8\\13x=2\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{8}{7}\\x=\frac{2}{13}\end{cases}}\)
a) Ta có: \(A=\left(4-x\right)\left(16+4x+x^2\right)-\left(4-x\right)^3\)
\(=64-x^3+\left(x-4\right)^3\)
\(=64-x^3+x^3-12x^2+48x-64\)
\(=-12x^2+48x\)
b) Ta có: \(B=\left(3x+2\right)\left(9x^2-6x+4\right)-\left(3x-2\right)\left(9x^2+6x+4\right)\)
\(=27x^3+8-27x^3+8\)
=16
c) Ta có: \(C=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)^2\)
\(=x^3+1-x\left(x^2+2x+1\right)\)
\(=x^3+1-x^3-2x^2-x\)
\(=-2x^2-x+1\)
a) \(\left(2x-y\right)\left(4x^2-2xy+y^2\right)\)
\(=8x^3-4x^2y+2xy^2-4xy^2+2xy^2-y^3\)
\(=8x^3-8x^2y+4xy^2-y^3\)
b) \(\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2\)
\(=2x^2-3xy+5y^2\)
a,x3+3x2+3x+1
b,x2+6x+9
c,-x3+9x2-27x+27
d,x2+4x+4
k,10x-25-x2
f,(x+y)2-9x2
g,8x3+42x2y+16xy2+6xy+y3
a) \(x^3+3x^2+3x+1=x^2+3\cdot x^2\cdot1+3\cdot x\cdot1^2+1^3=\left(x-1\right)^3\)
b) \(x^2+6x+9=x^2+2\cdot3\cdot x+3^2=\left(x+3\right)^2\)
c) \(-x^3+9x^2-27x+27\)
\(=-\left(x^3-9x^2+27x-27\right)\)
\(=-\left(x^3-3\cdot3\cdot x^2+3\cdot3^2\cdot x-3^3\right)=-\left(x-3\right)^3\)
d) \(x^2+4x+4=x^2+2\cdot2\cdot x+2^2=\left(x+2\right)^2\)
k) \(10x-25-x^2=-x^2+10x-25=-\left(x^2-10x+25\right)\)
\(=-\left(x^2-2\cdot5\cdot x+5^2\right)=-\left(x-5\right)^2\)
f) \(\left(x+y\right)^2-9x^2=\left(x-y\right)^2-\left(3x\right)^2=\left[\left(x-y\right)-3x\right]\left[\left(x-y\right)+3x\right]\)
\(=\left(x-y-3x\right)\left(x-y+3x\right)=\left(-2x-y\right)\left(4x-y\right)\)
a) Ta có: \(x^4-16x^2=0\)
\(\Leftrightarrow x^2\left(x^2-16\right)=0\)
\(\Leftrightarrow x^2\left(x-4\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=0\\x-4=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
Vậy: \(x\in\left\{0;4;-4\right\}\)
b) Ta có: \(9x^2+6x+1=0\)
\(\Leftrightarrow\left(3x\right)^2+2\cdot3x\cdot1+1^2=0\)
\(\Leftrightarrow\left(3x+1\right)^2=0\)
\(\Leftrightarrow3x+1=0\)
\(\Leftrightarrow3x=-1\)
hay \(x=-\frac{1}{3}\)
Vậy: \(x=-\frac{1}{3}\)
c) Ta có: \(x^2-6x=16\)
\(\Leftrightarrow x^2-6x-16=0\)
\(\Leftrightarrow x^2-8x+2x-16=0\)
\(\Leftrightarrow x\left(x-8\right)+2\left(x-8\right)=0\)
\(\Leftrightarrow\left(x-8\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-8=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-2\end{matrix}\right.\)
Vậy: \(x\in\left\{8;-2\right\}\)
d) Ta có: \(9x^2+6x=80\)
\(\Leftrightarrow9x^2+6x-80=0\)
\(\Leftrightarrow9x^2+6x+1-81=0\)
\(\Leftrightarrow\left(3x+1\right)^2-9^2=0\)
\(\Leftrightarrow\left(3x+1-9\right)\left(3x+1+9\right)=0\)
\(\Leftrightarrow\left(3x-8\right)\left(3x+10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-8=0\\3x+10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=8\\3x=-10\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{8}{3}\\x=-\frac{10}{3}\end{matrix}\right.\)
Vậy: \(x\in\left\{\frac{8}{3};-\frac{10}{3}\right\}\)
e) Ta có: \(25\left(2x-1\right)^2-9\left(x+1\right)^2=0\)
\(\Leftrightarrow\left(10x-5\right)^2-\left(3x+3\right)^2=0\)
\(\Leftrightarrow\left(10x-5-3x-3\right)\left(10x-5+3x+3\right)=0\)
\(\Leftrightarrow\left(7x-8\right)\left(13x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}7x-8=0\\13x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}7x=8\\13x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{8}{7}\\x=\frac{2}{13}\end{matrix}\right.\)
Vậy: \(x\in\left\{\frac{8}{7};\frac{2}{13}\right\}\)