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5 tháng 9 2020
Mấy bài dài dài kia tí mình làm cho :)
( x - 1 )3 - x( x - 2 )2 + 1
= x3 - 3x2 + 3x - 1 - x( x2 - 4x + 4 ) + 1
= x3 - 3x2 + 3x - x3 + 4x2 - 4x
= x2 - x = x( x - 1 )
2x( 3x + 2 ) - 3x( 2x + 3 )
= 6x2 + 4x - 6x2 - 9x
= -5x
( x + 2 )3 + ( x - 3 )2 - x2( x + 5 )
= x3 + 6x2 + 12x + 8 + x2 - 6x + 9 - x3 - 5x2
= 2x2 + 6x + 17
( 2x + 3 )( x - 5 ) + 2x( 3 - x ) + x - 10
= 2x2 - 7x - 15 + 6x - 2x2 + x - 10
= -25
( x + 5 )( x2 - 5x + 25 ) - x( x - 4 )2 + 16x
= x3 + 53 - x( x2 - 8x + 16 ) + 16x
= x3 + 125 - x3 + 8x2 - 16x + 16
= 8x2 + 125
( -x - 2 )3 + ( 2x - 4 )( x2 + 2x + 4 ) - x2( x - 6 )
= -x3 - 6x2 - 12x - 8 + 2x3 - 16 - x3 + 6x2
= -12x - 24 = -12( x + 2 )
A
5 tháng 9 2020
Tương tự ...
a, \(\left(x-1\right)^3-x\left(x-2\right)^2+1=x^3-3x^2+3x-1-x^3+4x^2-4x+1=x^2-x\)
b, \(2x\left(3x+2\right)-3x\left(2x+3\right)=6x^2+4x-6x^2-9x=-5x\)
c, \(\left(x+2\right)^3+\left(x-3\right)^2-x^2\left(x+5\right)=x^3+6x^2+12x+8+x^2+6x+9-x^3-5x^2=2x^2+18x+17\)
HC
0
CM
4 tháng 12 2018
Bài 1:
a) \(x^2+9y^2-y^4-6xy\)
\(=\left(x^2-6xy+9y^2\right)-y^4\)
\(=\left[x^2-2.x.3y+\left(3y\right)^2\right]-\left(y^2\right)^2\)
\(=\left(x-3y\right)^2-\left(y^2\right)^2\)
\(=\left(x-3y-y^2\right)\left(x-3y+y^2\right)\)
b) \(2x^2-x-28\)
\(=2x^2-8x+7x-28\)
\(=2x\left(x-4\right)+7\left(x-4\right)\)
\(=\left(x-4\right)\left(2x+7\right)\)
Bài 2:
a) \(2x\left(x^2-2x+3\right)-2x^3\)
\(=2x\left(x^2-2x+3-x^2\right)\)
\(=2x\left(3-2x\right)\)
b) \(2x\left(x-3\right)-\left(x+5\right)\left(2x-1\right)\)
\(=\left(2x^2-6x\right)-\left(2x^2+9x-5\right)\)
\(=2x^2-6x-2x^2-9x+5\)
\(=-15x+5\)
\(=-5\left(3x-1\right)\)
c) \(\left(5-x\right)^2+\left(x+5\right)^2-\left(2x+10\right)\left(x-5\right)\)
\(=\left(x-5\right)^2-2\left(x+5\right)\left(x-5\right)+\left(x+5\right)^2\)
\(=\left[\left(x-5\right)-\left(x+5\right)\right]^2\)
\(=\left(x-5-x-5\right)^2\)
\(=\left(-10\right)^2=100\)
Bài 3:
a) \(x-2=\left(x-2\right)^2\)
\(\Rightarrow\left(x-2\right)-\left(x-2\right)^2=0\)
\(\Rightarrow\left(x-2\right)\left(1-x+2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(3-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\3-x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
b) \(\left(-3x+9\right)x^2-7x+21=0\)
\(\Rightarrow-3\left(x-3\right)x^2-7\left(x-3\right)=0\)
\(\Rightarrow\left(x-3\right)\left(-3x^2-7\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\-3x^2-7=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x^2=-\dfrac{7}{3}\end{matrix}\right.\)
Mà x2 > 0 hoặc x2 = 0 với mọi x
=> x2 = -7/3 không thỏa mãn
=> x= 3
4 tháng 12 2018
Phân tích đa thức
a, x^2+9y^2-y^4-6xy
=(x^2-6xy+9y^2)-y^4
=(x-3y)^2-y^4
=(x-3y-y^2)(x-3y+y^2)
b, 2x^2-x-28
=(2x^2-8x)+(7x-28)
=2x(x-4)+7(x-4)
=(x-4)(2x+7)
Rút gọn
a,2x(x^2-2x+3)-2x^3
=2x(x^2-2x+3-x^2)
=2x(-2x+3)
b,2x(x-3)-(x+5)(2x-1)
=2x^2-6x-2x^2-9x+5
=-15x+5
=-5(3x-1)
c,(5-x)^2+(x+5)^2-(2x+10)(x-5)
Ta có:(5-x)^2=(x-5)^2
=(x-5)^2-2(x+5)(x-5)+(x+5)^2
=(x-5-x-5)^2
=100
Tìm x
a,x-2=(x-2)^2=0
=>x-2=0=>x=2
b,(-3x+9)x^2-7x+21=0
=>-3(x-3)x^2-7(x-3)=0
=>(x-3)(-3x^2-7)=0
=>\(\left[{}\begin{matrix}x-3=0=>x=3\\-3x^2-7=0=>x=\sqrt{\dfrac{-7}{3}}\end{matrix}\right.\)
14 tháng 1 2016
a)x=-17
b)x=9/10
c)x=4\(\frac{1}{3}\)
tick đi giải chi tiết cho
14 tháng 1 2016
a)Sử dụng tính chất tỉ lệ thức, có thể biến đổi phương trình như sau
7x+35/3=2x+6/1=>(7x+35)1=3(2x+6)
=>x=-17
b)Sử dụng tính chất tỉ lệ thức, có thể biến đổi phương trình như sau
17x+19/20=27x+10/20=>(17x+19)20=20(27x+10)
c)<=>(x-2)^3+(x-4)^3+(x-7)^3+(-3)(x-2)(x-4)(x-7)=19(3x-13)
=>19(3x-13)=0
rút gọn 57x=247
=>19.3x=19.13
=>3x=13
=>x=13/3
=>x=4\(\frac{1}{3}\)
HN
1 tháng 1 2018
a) \(\dfrac{x^2+2}{x^3-1}+\dfrac{2}{x^2+x+1}+\dfrac{1}{1-x}\)
\(=\dfrac{x^2+2}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{2}{x^2+x+1}-\dfrac{1}{x-1}\)
\(=\dfrac{x^2+2+2\left(x-1\right)-\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^2+2+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x-1}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{1}{x^2+x+1}\)
b) \(\dfrac{9}{x^3-9x}-\dfrac{-1}{x+3}\)
\(=\dfrac{9}{x\left(x-3\right)\left(x+3\right)}+\dfrac{1}{x+3}\)
\(=\dfrac{9+x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{9+x^2-3x}{x\left(x-3\right)\left(x+3\right)}\)
c) \(\dfrac{x^3-8}{5x+10}.\dfrac{x^2+4x}{x^2+2x+4}\)
\(=\dfrac{x\left(x-2\right)\left(x^2+2x+4\right)\left(x+4\right)}{5\left(x+2\right)\left(x^2+2x+4\right)}\)
\(=\dfrac{x\left(x-2\right)\left(x+4\right)}{5\left(x+2\right)}\)
d) \(\dfrac{5x+10}{4x-8}.\dfrac{4-2x}{x+2}\)
\(=\dfrac{5\left(x+2\right)}{4\left(x-2\right)}.\dfrac{2\left(2-x\right)}{x+2}\)
\(=-\dfrac{10\left(x+2\right)\left(x-2\right)}{4\left(x-2\right)\left(x+2\right)}\)
\(=-\dfrac{5}{2}\)
e) \(\dfrac{\left(x-13\right)^2}{2x^5}.\dfrac{-3x^2}{x-13}\)
\(=\dfrac{x-13}{2x^3}.\dfrac{-3}{1}\)
\(=\dfrac{-3\left(x-13\right)}{2x^3}\)
g) \(\dfrac{x^2+6x+9}{1-x}.\dfrac{\left(x-1\right)^2}{2\left(x+3\right)^2}\)
\(=-\dfrac{\left(x+3\right)^2}{x-1}.\dfrac{\left(x-1\right)^2}{2\left(x+3\right)^2}\)
\(=-\dfrac{\left(x+3\right)^2\left(x-1\right)^2}{2\left(x-1\right)\left(x+3\right)^2}\)
\(=-\dfrac{x-1}{2}\).
14 tháng 6 2022
a: \(B=\left(\dfrac{x+1}{2\left(x-1\right)}+\dfrac{3}{\left(x-1\right)\left(x+1\right)}-\dfrac{x+3}{2\left(x+1\right)}\right)\cdot\dfrac{4\left(x-1\right)\left(x+1\right)}{5}\)
\(=\dfrac{x^2+2x+1+6-x^2-2x+3}{2\left(x+1\right)\left(x-1\right)}\cdot\dfrac{4\left(x-1\right)\left(x+1\right)}{5}\)
\(=\dfrac{10}{1}\cdot\dfrac{2}{5}=10\cdot\dfrac{2}{5}=4\)
b: \(\dfrac{x^2-36}{2x+10}\cdot\dfrac{3}{6-x}\)
\(=\dfrac{\left(x-6\right)\left(x+6\right)}{2\left(x+5\right)}\cdot\dfrac{-3}{x-6}\)
\(=\dfrac{-3\left(x+6\right)}{2\left(x+5\right)}\)
c: \(\dfrac{5x+10}{4x-8}\cdot\dfrac{4-2x}{x+2}\)
\(=\dfrac{5\left(x+2\right)}{4\left(x-2\right)}\cdot\dfrac{-2\left(x-2\right)}{x+2}=\dfrac{-10}{4}=\dfrac{-5}{2}\)
d: \(\dfrac{1-4x^2}{x^2+4x}:\dfrac{2-4x}{3x}\)
\(=\dfrac{1-4x^2}{x\left(x+4\right)}\cdot\dfrac{3x}{2\left(1-2x\right)}\)
\(=\dfrac{\left(1-2x\right)\left(1+2x\right)}{x+4}\cdot\dfrac{3}{2\left(1-2x\right)}=\dfrac{3\left(2x+1\right)}{x+4}\)
\(\frac{1}{x-2}+\frac{x^2-x-2}{x^2-7x+10}-\frac{2x-4}{x-5}\\ \Leftrightarrow\frac{x-5}{x^2-7x+10}+\frac{x^2-x-2}{x^2-7x+10}-\frac{2x^2-8x+8}{x^2-7x+10}\\ \Leftrightarrow\frac{x-5+x^2-x-2-2x^2+8x-8}{x^2-7x+10}\\ \Leftrightarrow\frac{8x-x^2-15}{x^2-7x+10}\)