(4x-1)=3 mũ 2
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ND
2 tháng 6 2018
1. \(x^6-2x^3+1=0\Leftrightarrow\left(x^3-1\right)^2=0\Leftrightarrow x=1\)
2. \(x^6+\dfrac{1}{4}x^3+\dfrac{1}{64}=0\Leftrightarrow\left(x^3\right)^2+2.x^3.\dfrac{1}{8}+\left(\dfrac{1}{8}\right)^2=0\Leftrightarrow\left(x+\dfrac{1}{8}\right)^2=0\Leftrightarrow x=-\dfrac{1}{2}\)4. \(x^3-10x^2+25x=0\Leftrightarrow x^3-5x^2-5x^2+25x=0\)
\(\Leftrightarrow x^2\left(x-5\right)-5x\left(x-5\right)=0\)
\(\Leftrightarrow x\left(x-5\right)^2=0\Leftrightarrow x=5\)
5. \(\dfrac{1}{4}x^3-3x^2+9x=0\)
\(\Leftrightarrow x\left(\dfrac{1}{4}x^2-3x+9\right)=0\)
\(\Leftrightarrow x\left[\left(\dfrac{1}{2}x\right)^2-2.\dfrac{1}{2}x.3+3^2\right]=0\)
\(\Leftrightarrow x\left(\dfrac{1}{2}x-3\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)
6. \(x^5-16x=0\Leftrightarrow x\left(x^4-16\right)=0\Leftrightarrow x\left(x^2-4\right)\left(x^2+4\right)=0\)
\(\Leftrightarrow x\left(x-2\right)\left(x+2\right)\left(x^2+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2\\x^2=-4\left(l\right)\end{matrix}\right.\)
7. \(4x^2+4x-3=0\Leftrightarrow4x^2-2x^2-6x-3=0\)
\(\Leftrightarrow2x\left(2x-1\right)-3\left(2x-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(2x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)
8. \(4x^2+28x+48=0\Leftrightarrow4x^2+12x+14x+48=0\)
\(\Leftrightarrow4x\left(x+3\right)+12\left(x+4\right)=0\)
\(\Leftrightarrow\left(4x+12\right)\left(x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-4\end{matrix}\right.\)
9. \(9x^2-12x+3=0\Leftrightarrow9x^2-9x-3x+3=0\Leftrightarrow9x\left(x-1\right)-3\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(9x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{3}\end{matrix}\right.\)
21 tháng 9 2020
a) ( x - 3 )2 - 4 = 0
<=> ( x - 3 )2 - 22 = 0
<=> ( x - 3 - 2 )( x - 3 + 2 ) = 0
<=> ( x - 5 )( x - 1 ) = 0
<=> x = 5 hoặc x = 1
b( 2x + 3 )2 - ( 2x + 1 )( 2x - 1 ) = 22
<=> 4x2 + 12x + 9 - ( 4x2 - 1 ) = 22
<=> 4x2 + 12x + 9 - 4x2 + 1 = 22
<=> 12x + 10 = 22
<=> 12x = 12
<=> x = 1
c) ( 4x + 3 )( 4x - 3 ) - ( 4x - 5 )2 = 16
<=> 16x2 - 9 - ( 16x2 - 40x + 25 ) = 16
<=> 16x2 - 9 - 16x2 + 40x - 25 = 16
<=> 40x - 34 = 16
<=> 40x = 50
<=> x = 50/40 = 5/4
d) x3 - 9x2 + 27x - 27 = -8
<=> ( x - 3 )3 = -8
<=> ( x - 3 )3 = (-2)3
<=> x - 3 = -2
<=> x = 1
e) ( x + 1 )3 - x2( x + 3 ) = 2
<=> x3 + 3x2 + 3x + 1 - x3 - 3x2 = 2
<=> 3x + 1 = 2
<=> 3x = 1
<=> x = 1/3
f) ( x - 2 )3 - x( x - 1 )( x + 1 ) + 6x2 = 5
<=> x3 - 6x2 + 12x - 8 - x( x2 - 1 ) + 6x2 = 5
<=> x3 + 12x - 8 - x3 + x = 5
<=> 13x - 8 = 5
<=> 13x = 13
<=> x = 1
21 tháng 9 2020
a) \(\left(x-3\right)^2-4=0\)
=> \(\left(x-3\right)^2-2^2=0\)
=> \(\left(x-3-2\right)\left(x-3+2\right)=0\)
=> \(\left(x-5\right)\left(x-1\right)=0\)
=> \(\orbr{\begin{cases}x=5\\x=1\end{cases}}\)
b) \(\left(2x+3\right)^2-\left(2x+1\right)\left(2x-1\right)=22\)
=> \(\left(2x+3\right)^2-\left[\left(2x\right)^2-1^2\right]=22\)
=> \(\left(2x+3\right)^2-\left(4x^2-1\right)=22\)
=> \(\left(2x\right)^2+2\cdot2x\cdot3+3^2-4x^2+1=22\)
=> \(4x^2+12x+9-4x^2+1=22\)
=> \(12x+9+1=22\)
=> \(12x+10=22\)
=> 12x = 12
=> x = 1
c) \(\left(4x+3\right)\left(4x-3\right)-\left(4x-5\right)^2=16\)
=> \(\left(4x\right)^2-3^2-\left[\left(4x\right)^2-2\cdot4x\cdot5+5^2\right]=16\)
=> \(16x^2-9-\left(16x^2-40x+25\right)=16\)
=> \(16x^2-9-16x^2+40x-25=16\)
=> \(-9+40x-25=16\)
=> \(40x=16+25-\left(-9\right)=16+25+9=50\)
=> x = 50/40 = 5/4
d) \(x^3-9x^2+27x-27=-8\)
=> \(x^3-3\cdot x^2\cdot3+3\cdot x\cdot3^2-3^3=8\)
=> \(\left(x-3\right)^3=-8\)
=> \(\left(x-3\right)^3=\left(-2\right)^3\)
=> x - 3 = -2 => x = 1
e) \(\left(x+1\right)^3-x^2\left(x+3\right)=2\)
=> \(x^3+3x^2+3x+1-x^3-3x^2=2\)
=> \(3x+1=2\)
=> \(3x=1\)=> x = 1/3
f) \(\left(x-2\right)^3-x\left(x-1\right)\left(x+1\right)+6x^2=5\)
=> \(x^3-3\cdot x^2\cdot2+3\cdot x\cdot2^2-2^3-x\left(x^2-1\right)+6x^2=5\)
=> \(x^3-6x^2+12x-8-x^3+x+6x^2=5\)
=> \(\left(12x+x\right)-8=5\)
=> 13x = 13
=> x = 1
9 tháng 8 2021
1, \(x^3+4x^2+4x=0\Leftrightarrow x\left(x^2+4x+4\right)=0\)
\(\Leftrightarrow x\left(x+2\right)^2=0\Leftrightarrow x=-2;x=0\)
2, \(\left(x+3\right)^2-4=0\Leftrightarrow\left(x+3-2\right)\left(x+3+2\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+5\right)=0\Leftrightarrow x=-5;x=1\)
3, \(x^4-9x^2=0\Leftrightarrow x^2\left(x^2-9\right)=0\)
\(\Leftrightarrow x^2\left(x-3\right)\left(x+3\right)=0\Leftrightarrow x=0;\pm3\)
4, \(x^2-6x+9=81\Leftrightarrow\left(x-3\right)^2=9^2\)
\(\Leftrightarrow\left(x-3-9\right)\left(x-3+9\right)=0\Leftrightarrow\left(x-12\right)\left(x+6\right)=0\Leftrightarrow x=-6;x=12\)
5, em xem lại đề nhé
9 tháng 8 2021
à lag tý @@
5, \(x^3+6x^2+9x-4x=0\Leftrightarrow x^3+6x^2+5x=0\)
\(\Leftrightarrow x\left(x^2+6x+5\right)=0\Leftrightarrow x\left(x^2+x+5x+5\right)=0\)
\(\Leftrightarrow x\left(x+1\right)\left(x+5\right)=0\Leftrightarrow x=-5;x=-1;x=0\)
NH
1 tháng 9 2020
\(\text{a)}\Rightarrow x-1-x-1-x+2=5\)
\(\Rightarrow-x=5\)
\(\Rightarrow x=-5\)
\(\text{Vậy x=-5}\)
\(\text{b)}\left(2x-1\right)^2-\left(2x+3\right)^2=7\)
\(\Rightarrow\left(4x^2-4x+1\right)-\left(4x^2+12x+9\right)=7\)
\(\Rightarrow4x^2-4x+1-4x^2-12x-9=7\)
\(\Rightarrow-16x-8=7\)
\(\Rightarrow-16x=15\)
\(\Rightarrow x=\frac{-15}{16}\)
\(\text{Vậy }x=\frac{-15}{16}\)
\(\text{c)}\Rightarrow16x^2-9-\left(16x^2-8x+1\right)=8\)
\(\Rightarrow-9+8x-1=8\)
\(\Rightarrow8x=18\)
\(\Rightarrow x=\frac{18}{8}=\frac{9}{4}\)
\(\text{Vậy }x=\frac{9}{4}\)
\(\text{Phần d số rất lẻ, có thể bạn chép sai đề nên mình ko chữa nha~}\)
7 tháng 8 2016
a) \(\left(6x-5y\right)^2=36x^2-60xy+25y^2\)
b) \(\left(4x-1\right)^2=16x^2-8x+1\)
c) \(\left(x+2\right)^2=x^2+4x+4\)
d) \(x^2-64=\left(x-8\right)\left(x+8\right)\)
e) \(4x^2-64=\left(2x-8\right)\left(2x+8\right)\)
f) \(25x^2-4=\left(5x-2\right)\left(5x+2\right)\)
g) \(\left(x+1\right)^3=x^3+3x^2+3x+1\)
h) \(\left(x-3\right)^3=x^3-9x^2+27x-27\)
k) \(x^3+8=\left(x+2\right)\left(x^2-2x+4\right)\)
l) \(x^3-125=\left(x-5\right)\left(x^2+5x+25\right)\)
y) \(27y^3-1=\left(3y-1\right)\left(9y^2+3y+1\right)\)
5 tháng 8 2021
f) = x2( x - 4 ) - 9( x - 4 ) = ( x - 4 )( x - 3 )( x + 3 )
g) = 4( x - y ) + ( x - y )2 = ( x - y )( x - y + 4 )
h) = x3( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x3 + x - 1 )
i) = ( x - y )( x + y ) - 4( x + y ) = ( x + y )( x - y - 4 )
j) = ( x - y )( x2 + xy + y2 ) - 3( x - y ) = ( x - y )( x2 + xy + y2 - 3 )
QA
5 tháng 8 2021
Trả lời:
f, x3 - 4x2 - 9x + 36 = ( x3 - 4x2 ) - ( 9x - 36 ) = x2 ( x - 4 ) - 9 ( x - 4 ) = ( x - 4 )( x2 - 9 ) = ( x - 4 )( x - 3 )( x + 3 )
g, 4x - 4y + x2 - 2xy + y2 = ( 4x - 4y ) + ( x2 - 2xy + y2 ) = 4 ( x - y ) + ( x - y )2 = ( x - y ) ( 4 + x - y )
h, x4 + x3 + x2 - 1 = ( x4 + x3 ) + ( x2 - 1 ) = x3 ( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x3 + x - 1 )
i, x2 - y2 - 4x - 4y = ( x2 - y2 ) - ( 4x + 4y ) = ( x - y )( x + y ) - 4 ( x + y ) = ( x + y )( x - y - 4 )
j, x3 - y3 - 3x + 3y = ( x3 - y3 ) - ( 3x - 3y ) = ( x - y )( x2 + xy + y2 ) - 3 ( x - y ) = ( x - y )( x2 + xy + y2 - 3 )
21 tháng 9 2020
a) 2( x - 1 )2 - 4( 3 + x )2 + 2x( x - 5 )
= 2( x2 - 2x + 1 ) - 4( 9 + 6x + x2 ) + 2x2 - 10x
= 2x2 - 4x + 2 - 36 - 24x - 4x2 + 2x2 - 10x
= ( 2x2 - 4x2 + 2x2 ) + ( -4x - 24x - 10x ) + ( 2 - 36 )
= -38x - 34
b) 2( 2x + 5 )2 - 3( 4x + 1 )( 1 - 4x )
= 2( 4x2 + 20x + 25 ) + 3( 4x + 1 )( 4x - 1 )
= 8x2 + 40x + 50 + 3( 16x2 - 1 )
= 8x2 + 40x + 50 + 48x2 - 3
= 56x2 + 40x + 47
c) ( x - 1 )3 - x( x - 3 )2 + 1
= x3 - 3x2 + 3x - 1 - x( x2 - 6x + 9 ) + 1
= x3 - 3x2 + 3x - x3 + 6x2 - 9x
= 3x2 - 6x
d) ( x + 2 )3 - x2( x + 6 )
= x3 + 6x2 + 12x + 8 - x3 - 6x2
= 12x + 8
e) ( x - 2 )( x + 2 ) - ( x + 1 )3 - 2x( x - 1 )2
= x2 - 4 - ( x3 + 3x2 + 3x + 1 ) - 2x( x2 - 2x + 1 )
= x2 - 4 - x3 - 3x2 - 3x - 1 - 2x3 + 4x2 - 2x
= -3x3 + 2x2 - 5x - 5
f) ( a + b - c )2 - ( b - c )2 - 2a( b - c )
= [ ( a + b ) - c ]2 - ( b2 - 2bc + c2 ) - 2ab + 2ac
= [ ( a + b )2 - 2( a + b )c + c2 ] - b2 + 2bc - c2 - 2ab + 2ac
= a2 + 2ab + b2 - 2ac - 2bc + c2 - b2 + 2bc - c2 - 2ab + 2ac
= a2
21 tháng 9 2020
a) \(2\left(x-1\right)^2-4\left(3+x\right)^2+2x\left(x-5\right)\)
Dùng hẳng đẳng thức thứ nhất + hai :
= \(2\left(x^2-2\cdot x\cdot1+1^2\right)-4\left(3^2+2\cdot3\cdot x+x^2\right)+2x^2-10x\)
= \(2\left(x^2-2x+1\right)-4\left(9+6x+x^2\right)+2x^2-10x\)
= \(2x^2-4x+2-36-24x-4x^2+2x^2-10x\)
= \(-38x-34\)
b) 2(2x + 5)2 - 3(4x + 1)(1 - 4x)
Dùng đẳng thức thứ 1 + 3
= 2[(2x)2 + 2.2x.5 + 52 ] - (-3)[(4x)2 - 12 ]
= 2(4x2 + 20x + 25) - (-3).(16x2 - 1)
= 8x2 + 40x + 50 - (3 - 48x2)
= 8x2 + 40x + 50 - 3 + 48x2
= 56x2 + 40x + 47
c) (x - 1)3 - x(x - 3)2 + 1
Dùng đẳng thức 2 + 5:
= x3 - 3.x2.1 + 3.x.12 - 13 - x(x2 - 2.x.3 + 32) + 1
= x3 - 3x2 + 3x - 1 - x3 + 6x2 - 9x + 1
= (x3 - x3) + (-3x2 + 6x2) + (3x - 9x) + (-1 + 1)
= 3x2 - 6x
d) (x + 2)3 - x2(x + 6)
= x3 + 3.x2.2 + 3.x.22 + 23 - x3 - 6x2
= x3 + 6x2 + 12x + 8 - x3 - 6x2
= (x3 - x3) + (6x2 - 6x2) + 12x + 8 = 12x + 8
e) Dùng đẳng thức thứ 3,4 và 2
= x2 - 4 - (x3 + 3.x2.1 + 3.x.12 + 13) - 2x(x2 - 2.x.1 + 12)
= x2 - 4 - (x3 + 3x2 + 3x + 1) - 2x3 + 4x2 - 2x
= x2 - 4 - x3 - 3x2 - 3x - 1 - 2x3 + 4x2 - 2x
= (x2 - 3x2 + 4x2) + (-4 - 1) + (-x3 - 2x3) + (-3x - 2x)
= 2x2 - 5 - 3x3 - 5x
f) Đặt \(a+b-c=A\)
\(b-c=B\)
= \(A^2-B^2-2AB\)
= \(A^2-2AB+\left(-B\right)^2\)
\(=A^2-2AB+B^2\)
= (A - B)2
= (a + b - c - (b - c))2
= (a + b - c - b + c)2
= a2
(4x-1)=3 mũ 2
4x-1 = 9
4x = 9 + 1
4x = 10
x = 10:4
x = 2,5
HT và $$$
---> 4x - 1 = 9
---> 4x = 10
---> x = 5/2
xin tiick