Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
1,
a, = 2x.(x-2)
b, = (x^2+y^2+2xy)-(2x+2y)
= (x+y)^2-2.(x+y)
= (x+y).(x+y-2)
2,
a,<=> x^2-1-x^2-2x = 3
<=> -2x-1=3
<=> -2x=4
<=> x=4 : (-2) = -2
b, <=>(x^2-4x+4)-7=0
<=>(x-2)^2-7=0
<=> (x-2)^2=7
=> x-2=+-\(\sqrt{7}\)
<=> x=2+-\(\sqrt{7}\)
k mk nha
a, \(2x-4x\)
\(=-2x\)
b, \(x^2+y^2+2xy-2x-2y\)
\(=\left(x+y\right)^2-2\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y-2\right)\)
a, \(\left(x+1\right)\left(x-1\right)-x\left(x+2\right)=3\)
\(\Leftrightarrow x^2-1-x^2-2x=3\)
\(\Leftrightarrow-2x=4\)
\(\Leftrightarrow x=-2\)
b,\(x^2-4x+3=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x-3=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=1\\x=3\end{cases}}\)
Bài 1:
a, x2-3xy-10y2
=x2+2xy-5xy-10y2
=(x2+2xy)-(5xy+10y2)
=x(x+2y)-5y(x+2y)
=(x+2y)(x-5y)
b, 2x2-5x-7
=2x2+2x-7x-7
=(2x2+2x)-(7x+7)
=2x(x+1)-7(x+1)
=(x+1)(2x-7)
Bài 2:
a, x(x-2)-x+2=0
<=>x(x-2)-(x-2)=0
<=>(x-2)(x-1)=0
<=>\(\orbr{\begin{cases}x-2=0\\x-1=0\end{cases}}\)<=>\(\orbr{\begin{cases}x=2\\x=1\end{cases}}\)
b, x2(x2+1)-x2-1=0
<=>x2(x2+1)-(x2+1)=0
<=>(x2+1)(x2-1)=0
<=>x2+1=0 hoặc x2-1=0
1, x2+1=0 2, x2-1=0
<=>x2= -1(loại) <=>x2=1
<=>x=1 hoặc x= -1
c, 5x(x-3)2-5(x-1)3+15(x+2)(x-2)=5
<=>5x(x-3)2-5(x-1)3+15(x2-4)=5
<=>5x(x2-6x+9)-5(x3-3x2+3x-1)+15x2-60=5
<=>5x3-30x2+45x-5x3+15x2-15x+5+15x2-60=5
<=>30x-55=5
<=>30x=55+5
<=>30x=60
<=>x=2
d, (x+2)(3-4x)=x2+4x+4
<=>(x+2)(3-4x)=(x+2)2
<=>(x+2)(3-4x)-(x+2)2=0
<=>(x+2)(3-4x-x-2)=0
<=>(x+2)(1-5x)=0
<=>\(\orbr{\begin{cases}x+2=0\\1-5x=0\end{cases}}\)<=>\(\orbr{\begin{cases}x=-2\\-5x=-1\end{cases}}\)<=>\(\orbr{\begin{cases}x=-2\\x=\frac{-1}{-5}\end{cases}}\)<=>\(\orbr{\begin{cases}x=-2\\x=\frac{1}{5}\end{cases}}\)
Bài 3:
a, Sắp xếp lại: x3+4x2-5x-20
Thực hiện phép chia ta được kết quả là x2-5 dư 0
b, Sau khi thực hiện phép chia ta được :
Để đa thức x3-3x2+5x+a chia hết cho đa thức x-3 thì a+15=0
=>a= -15
Bài 1:tìm x ,biết:
a) (2x - 1)(3x + 2) - 6x(x + 1) = 0
\(\Leftrightarrow6x^2+x-2-6x^2-6x=0\)
\(\Leftrightarrow-5x=2\)
\(\Leftrightarrow x=\frac{-2}{5}\)
b) \(\left(4x-1\right)^2-\left(2x+1\right)\left(8x-3\right)=0\)
\(\Leftrightarrow16x^2-8x+1-16x^2-2x+3=0\)
\(\Leftrightarrow-10x=-4\)
\(\Leftrightarrow x=\frac{2}{5}\)
c) \(4x^2-1=2\left(2x+1\right)\)
\(\Leftrightarrow\left(2x+1\right)\left(2x-1\right)-2\left(2x+1\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(2x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=\frac{3}{2}\end{cases}}\)
2a) \(4x^2-9y^2-6y-1=4x^2-\left(3y+1\right)^2\)
\(=\left(2x-3y-1\right)\left(2x+3y+1\right)\)
b) \(4x^2-1-2x\left(2x-1\right)=\left(2x-1\right)\left(2x+1\right)-2x\left(2x-1\right)\)
\(=1.\left(2x-1\right)\)
c) \(x^2-8x-4y^2+16=\left(x-4\right)^2-4y^2\)
\(=\left(x-4-2y\right)\left(x-4+2y\right)\)
d) \(9x^2-12x-y^2+4=\left(3x-2\right)^2-y^2\)
\(=\left(3x-2-y\right)\left(3x-2+y\right)\)
e) \(4x^2+10x-5=4x^2+2.2.\frac{5}{2}x+\frac{25}{4}-\frac{25}{4}-5\)
\(=\left(2x+\frac{5}{2}\right)^2-\frac{45}{4}\)
\(=\left(2x+\frac{5+3\sqrt{5}}{2}\right)\left(2x+\frac{5-3\sqrt{5}}{2}\right)\)
a, 4x2 - 12x + 9
= (2x + 3)2
b, 9x4y3 + 3x2y4
= 3x2y3(3x2 + y)
c, ( x - 3 )2 - 2x ( x - 3 )
= (x - 3)(x - 3 - 2x)
= (x - 3)(-x - 3)
d, 3x ( x - 1 ) + 6 ( x - 1 )
= 3(x - 1)(x + 2)
e, 2x ( x + 1 ) - 4x - 4
= 2x(x + 1) - 4(x + 1)
= (x + 1)(2x - 4)
= 2(x + 1)(x - 2)
f, ( 2x - 3 )2 - 4x + 6
= (2x - 3)2 - 2(2x - 3)
= (2x - 3)(2x - 3 - 2)
= (2x - 3)(2x - 5)
Mấy câu trên dễ
\(M=4a^2-6a+12\)
\(M=\left(2a\right)^2-2\cdot2a\cdot\frac{3}{2}+\left(\frac{3}{2}\right)^2+\frac{39}{4}\)
\(M=\left(2a-\frac{3}{2}\right)^2+\frac{39}{4}\ge\frac{39}{4}\forall x\left(đpcm\right)\)
1. a) 2x2y - 3xy2 - 6x + 9y = 2x( xy - 3 ) - 3y ( xy - 3) = ( 2x - 3y)(xy - 3)
b) x2 - 2x + 8 = x2 - 2x + 12 - 1 + 9 = ( x - 1 )2 + 32 ( xem lại đề bài )
2. a) ( 2x - 1) 2 - (2x-1)(2x+3) = 5
(2x-1)(2x-1-2x-3) = 5
-4(2x-1) = 5
2x - 1 = -1,25
2x = -0,25
x= -0,125
b) x(x-9 ) = 0
x= 0 hoặc x = 9
c, ko hiểu
3, M = (2a)2 - 2.2a.1,5 + ( 1,5)2 + 9,75
M= ( 2a - 1,5)2 + 9,75
Vì ( 2a - 1,5 )2 \(\ge\)0 \(\forall x\)
\(\Rightarrow\)( 2a - 1,5)2 + 9,75 \(\ge9,75\forall x\)
Vậy biểu thức trên luôn dương
a. 3x2+3xy-x-y
= (3x2+3xy)-(x-y)
= 3x(x+y)-(x+y) (sau dấu trừ đổi dấu)
=(x+y)(3x-1)
(x+1)2+2x(x-2)=3(x+4)(x+1)
<= >(x2+2x+1)+2x2-4x=(3x+12)(x+1)
<=>x2+2x+1+2x2-4x=3x2+3x+12x+12
<=>x2+2x+2x2-4x-3x2-3x-12x=12-1
<=>-17x=11
<=>x=\(\frac{-11}{17}\)
4x2-1+x(2x-1)=0
<=>4x2-1+2x2-x=0
<=> 6x2-x-1=0
<=>(6x2-x)-1=0
<=>x (6x-1) =1
<=>\(6x=2\)
<=>x=\(\frac{2}{6}=\frac{1}{3}\)
^-^