K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Các câu hỏi dưới đây có thể giống với câu hỏi trên
TM
3 tháng 7 2017
3) \(\left(x-3\right)\left(x+3\right)\left(x^2+9\right)-\left(x^2-2\right)\left(x^2+2\right)\)
\(=\left(x^2-9\right)\left(x^2+9\right)-\left(x^4-4\right)\)
\(=\left(x^4-81\right)-\left(x^4-4\right)\)
\(=x^4-81-x^4+4\)
=-77 =>đpcm
4)\(\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)
\(=\left[\left(3x+1\right)-\left(3x+5\right)\right]^2\)
\(=\left(3x+1-3x-5\right)^2\)
=(-4)2
=16 => đpcm
TM
3 tháng 7 2017
1)\(\left(x-2\right)^2-\left(x-3\right)\left(x-1\right)=\left(x^2-4x+4\right)-\left(x^2-4x+3\right)=1\)
=>đpcm
2)\(\left(x-1\right)^3-\left(x+1\right)^3+6\left(x+1\right)\left(x-1\right)\)
\(=\left(x-1-x-1\right)\left[\left(x-1\right)^2+\left(x-1\right)\left(x+1\right)+\left(x+1\right)^2\right]+6\left(x^2-1\right)\)
\(=\left(-2\right)\left(x^2-2x+1+x^2-1+x^2+2x+1\right)+6x^2-6\)
\(=\left(-2\right)\left(3x^2+1\right)+6x^2-6=-6x^2-2+6x^2-6=-8\) => đpcm
4 tháng 7 2017
Ta có : (a + b)(a2 - ab + b2) - 2a(a - b)2
= (a + b).(a - b)2 - 2a(a - b)2
= (a - b)2(a + b - 2a)
NN
a) 5x2- 4. ( x2-2x + 1 ) - 5 = 0
b) ( x2- 9 ) 2 - (x-3)2 = 0
c) x3- 3x + 2 = 0
giúp mik vs ~ mai kt~
2
DP
5 tháng 10 2017
a, \(5x^2-4\left(x^2-2x+1\right)-5=0\)
\(\Rightarrow5x^2-4x^2+8x-4-5=0\)
\(\Rightarrow x^2-x+9x-9=0\)
\(\Rightarrow x\left(x-1\right)+9\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x+9\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x+9=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-9\end{matrix}\right.\)
b, \(\left(x^2-9\right)^2-\left(x-3\right)^2=0\)
\(\Rightarrow\left(x^2-9-x+3\right)\left(x^2-9+x-3\right)=0\)
\(\Rightarrow\left(x^2-x-6\right)\left(x^2+x-12\right)=0\)
\(\Rightarrow\left(x^2-3x+2x-6\right)\left(x^2+4x-3x-12\right)=0\)
\(\Rightarrow\left[x\left(x-3\right)+2\left(x-3\right)\right]\left[x\left(x+4\right)-3\left(x+4\right)\right]=0\)
\(\Rightarrow\left(x-3\right)\left(x+2\right)\left(x+4\right)\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x+2=0\\x+4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\\x=-4\end{matrix}\right.\)
c, \(x^3-3x+2=0\)
\(\Rightarrow x^3+2x^2-2x^2-4x+x+2=0\)
\(\Rightarrow x^2\left(x+2\right)-2x\left(x+2\right)+\left(x+2\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x^2-2x+1\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x-1\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x+2=0\\\left(x-1\right)^2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-2\\x=1\end{matrix}\right.\)
NN
5 tháng 10 2017
a, 5x2−4(x2−2x+1)−5=05x2−4(x2−2x+1)−5=0
⇒5x2−4x2+8x−4−5=0⇒5x2−4x2+8x−4−5=0
⇒x2−x+9x−9=0⇒x2−x+9x−9=0
⇒x(x−1)+9(x−1)=0⇒x(x−1)+9(x−1)=0
⇒(x−1)(x+9)=0⇒(x−1)(x+9)=0
⇒[x−1=0x+9=0⇒[x=1x=−9⇒[x−1=0x+9=0⇒[x=1x=−9
b, (x2−9)2−(x−3)2=0(x2−9)2−(x−3)2=0
⇒(x2−9−x+3)(x2−9+x−3)=0⇒(x2−9−x+3)(x2−9+x−3)=0
⇒(x2−x−6)(x2+x−12)=0⇒(x2−x−6)(x2+x−12)=0
⇒(x2−3x+2x−6)(x2+4x−3x−12)=0⇒(x2−3x+2x−6)(x2+4x−3x−12)=0
⇒[x(x−3)+2(x−3)][x(x+4)−3(x+4)]=0⇒[x(x−3)+2(x−3)][x(x+4)−3(x+4)]=0
⇒(x−3)(x+2)(x+4)(x−3)=0⇒(x−3)(x+2)(x+4)(x−3)=0
⇒⎡⎢⎣x−3=0x+2=0x+4=0⇒⎡⎢⎣x=3x=−2x=−4⇒[x−3=0x+2=0x+4=0⇒[x=3x=−2x=−4
c, x3−3x+2=0x3−3x+2=0
⇒x3+2x2−2x2−4x+x+2=0⇒x3+2x2−2x2−4x+x+2=0
⇒x2(x+2)−2x(x+2)+(x+2)=0⇒x2(x+2)−2x(x+2)+(x+2)=0
⇒(x+2)(x2−2x+1)=0⇒(x+2)(x2−2x+1)=0
⇒(x+2)(x−1)2=0⇒(x+2)(x−1)2=0
⇒[x+2=0(x−1)2=0⇒[x=−2x=1⇒[x+2=0(x−1)2=0⇒[x=−2x=1
7 tháng 9 2018
\(\left(x-1\right)\left(x^3+bx^2+ax-2\right)\)
\(=x^4+bx^3+ax^2-2x-x^3-bx^2-ax+2\)
\(=x^4+x^3\left(b-1\right)+x^2\left(a-b\right)-x\left(a+2\right)+2\)
Đồng nhất với đa thức \(x^4-3x+2\), ta có:
\(b-1=0,a-b=0,a+2=3\)
\(\Rightarrow a=1,b=1\)
Chúc bạn học tốt.
17 tháng 8 2016
cái này là phép toán dễ mà, chỉ cần nắm vũng kiến thức trong chương 1 sách lớp 8 là đc có j đâu?
29 tháng 8 2020
Bài 1:
a) Ta có: \(VT=\frac{-u^2+3u-2}{\left(u+2\right)\left(u-1\right)}\)
\(=\frac{-\left(u^2-3u+2\right)}{\left(u+2\right)\left(u-1\right)}\)
\(=\frac{-\left(n^2-u-2u+2\right)}{\left(u+2\right)\left(u-1\right)}\)
\(=\frac{-\left[u\left(u-1\right)-2\left(u-1\right)\right]}{\left(u+2\right)\left(u-1\right)}\)
\(=\frac{-\left(u-1\right)\left(u-2\right)}{\left(u+2\right)\left(u-1\right)}\)
\(=\frac{2-u}{u+2}\)(1)
Ta có: \(VP=\frac{u^2-4u+4}{4-u^2}\)
\(=\frac{\left(u-2\right)^2}{-\left(u-2\right)\left(u+2\right)}\)
\(=\frac{-\left(u-2\right)}{u+2}\)
\(=\frac{2-u}{u+2}\)(2)
Từ (1) và (2) suy ra \(\frac{-u^2+3u-2}{\left(u+2\right)\left(u-1\right)}=\frac{u^2-4u+4}{4-u^2}\)
b) Ta có: \(VT=\frac{v^3+27}{v^2-3v+9}\)
\(=\frac{\left(v+3\right)\left(v^3-3u+9\right)}{v^2-3u+9}\)
\(=v+3=VP\)(đpcm)
Bài 2:
a) Ta có: \(\frac{3x^2-2x-5}{M}=\frac{3x-5}{2x-3}\)
\(\Leftrightarrow\frac{3x^2-5x+3x-5}{M}=\frac{3x-5}{2x-3}\)
\(\Leftrightarrow\frac{x\left(3x-5\right)+\left(3x-5\right)}{M}=\frac{3x-5}{2x-3}\)
\(\Leftrightarrow\frac{\left(3x-5\right)\left(x+1\right)}{M}=\frac{3x-5}{2x-3}\)
\(\Leftrightarrow M=\frac{\left(3x-5\right)\left(x+1\right)\left(2x-3\right)}{3x-5}\)
\(\Leftrightarrow M=\left(x+1\right)\left(2x-3\right)\)
\(\Leftrightarrow M=2x^2-3x+2x-3\)
hay \(M=2x^2-x-3\)
Vậy: \(M=2x^2-x-3\)
b) Ta có: \(\frac{2x^2+3x-2}{x^2-4}=\frac{M}{x^2-4x+4}\)
\(\Leftrightarrow\frac{2x^2+4x-x-2}{\left(x-2\right)\left(x+2\right)}=\frac{M}{\left(x-2\right)^2}\)
\(\Leftrightarrow\frac{2x\left(x+2\right)-\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\frac{M}{\left(x-2\right)^2}\)
\(\Leftrightarrow\frac{\left(x+2\right)\left(2x-1\right)}{\left(x+2\right)\left(x-2\right)}=\frac{M}{\left(x-2\right)^2}\)
\(\Leftrightarrow\frac{M}{\left(x-2\right)^2}=\frac{2x-1}{x-2}\)
\(\Leftrightarrow M=\frac{\left(2x-1\right)\left(x-2\right)^2}{\left(x-2\right)}\)
\(\Leftrightarrow M=\left(2x-1\right)\left(x-2\right)\)
\(\Leftrightarrow M=2x^2-4x-x+2\)
hay \(M=2x^2-5x+2\)
Vậy: \(M=2x^2-5x+2\)
Bài 3:
a) Ta có: \(\frac{x+1}{N}=\frac{x^2-2x+4}{x^3+8}\)
\(\Leftrightarrow\frac{x+1}{N}=\frac{x^2-2x+4}{\left(x+2\right)\left(x^2-2x+4\right)}\)
\(\Leftrightarrow\frac{x+1}{N}=\frac{1}{x+2}\)
\(\Leftrightarrow N=\left(x+1\right)\left(x+2\right)\)
hay \(N=x^2+3x+2\)
Vậy: \(N=x^2+3x+2\)
n) Ta có: \(\frac{\left(x-3\right)\cdot N}{3+x}=\frac{2x^3-8x^2-6x+36}{2+x}\)
\(\Leftrightarrow\frac{N\cdot\left(x-3\right)}{x+3}=\frac{2x^3+4x^2-12x^2-24x+18x+36}{x+2}\)
\(\Leftrightarrow\frac{N\cdot\left(x-3\right)}{\left(x+3\right)}=\frac{2x^2\left(x+2\right)-12x\left(x+2\right)+18\left(x+2\right)}{x+2}\)
\(\Leftrightarrow\frac{N\cdot\left(x-3\right)}{x+3}=\frac{\left(x+2\right)\left(2x^2-12x+18\right)}{x+2}\)
\(\Leftrightarrow\frac{N\cdot\left(x-3\right)}{x+3}=2x^2-12x+18\)
\(\Leftrightarrow\frac{N\cdot\left(x-3\right)}{x+3}=2x^2-6x-6x+18=2x\left(x-3\right)-6\left(x-3\right)=2\cdot\left(x-3\right)^2\)
\(\Leftrightarrow N\cdot\left(x-3\right)=\frac{2\left(x-3\right)^2}{x+3}\)
\(\Leftrightarrow N=\frac{2\left(x-3\right)^2}{x+3}:\left(x-3\right)=\frac{2\left(x-3\right)^2}{\left(x+3\right)\left(x-3\right)}\)
\(\Leftrightarrow N=\frac{2\left(x-3\right)}{x+3}\)
hay \(N=\frac{2x-6}{x+3}\)
Vậy: \(N=\frac{2x-6}{x+3}\)
27 tháng 7 2018
Ukm
It's very hard
l can't do it
Sorry!
27 tháng 7 2018
a) \(x^4-x^3-7x^2+x+6=0\)
\(\Leftrightarrow x^4+2x^3-3x^3-6x^2-x^2-2x+3x+6=0\)
\(\Leftrightarrow x^3\left(x+2\right)-3x^2\left(x+2\right)-x\left(x+2\right)+3\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^3-3x^2-x+3\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left[x^2\left(x-3\right)-\left(x-3\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)\left(x^2-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x-3\right)=0\). Làm nốt
b) \(2x^2+2xy+y^2+9=6x-\left|y+3\right|\)
\(\Leftrightarrow2x^2+2xy+y^2+9-6x+\left|y+3\right|=0\)
\(\Leftrightarrow\left(x^2+2xy+y^2\right)+x^2-6x+9+\left|y+3\right|=0\)
\(\Leftrightarrow\left(x+y\right)^2+\left(x-3\right)^2+\left|y+3\right|=0\)
Do \(\left(x+y\right)^2\ge0;\left(x-3\right)^2\ge0;\left|y+3\right|\ge0\forall x;y\)
\(\Rightarrow\hept{\begin{cases}x+y=0\\x-3=0\\y+3=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=3\\y=-3\end{cases}}\)
c) \(\left(2x^2+x\right)^2-4\left(2x^2+x\right)+3=0\)
\(\Leftrightarrow\left(2x^2+x\right)^2-2.\left(2x^2+x\right).2+4-1=0\)
\(\Leftrightarrow\left(2x^2+x-2\right)^2=1\Leftrightarrow\orbr{\begin{cases}2x^2+x-2=1\\2x^2+x-2=-1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x^2+x-3=0\\2x^2+x-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x^2+2.x.\frac{1}{4}+\frac{1}{16}-\frac{1}{16}-\frac{3}{2}=0\\x^2+2.x.\frac{1}{4}+\frac{1}{16}-\frac{1}{16}-\frac{1}{2}=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x+\frac{1}{4}\right)^2-\frac{25}{16}=0\\\left(x+\frac{1}{4}\right)^2-\frac{9}{16}=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}\left(x+\frac{1}{4}\right)^2=\frac{25}{16}\\\left(x+\frac{1}{4}\right)^2=\frac{9}{16}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{4}=\pm\frac{5}{4}\\x+\frac{1}{4}=\pm\frac{3}{4}\end{cases}}\)
Từ đó tính đc x
d) \(\left(x^2+3x+2\right)\left(x^2+7x+12\right)=24\)
\(\Leftrightarrow\left(x^2+x+2x+2\right)\left(x^2+3x+4x+12\right)=24\)
\(\Leftrightarrow\left[x\left(x+1\right)+2\left(x+1\right)\right]\left[x\left(x+3\right)+4\left(x+3\right)\right]=24\)
\(\Leftrightarrow\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24=0\)
\(\Leftrightarrow\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24=0\)
Đặt \(x^2+5x+5=a\), khi đó pt có dạng:
\(\left(a-1\right)\left(a+1\right)-24=0\Leftrightarrow a^2-1-24=0\)
\(\Leftrightarrow a^2-25=0\Leftrightarrow\left(a-5\right)\left(a+5\right)=0\Leftrightarrow\orbr{\begin{cases}a=5\\a=-5\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x^2+5x+5=5\\x^2+5x+5=-5\end{cases}}\Leftrightarrow\orbr{\begin{cases}x\left(x+5\right)=0\\x^2+5x+10=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x\left(x+5\right)=0\\x^2+2.x.\frac{5}{2}+\frac{25}{4}+\frac{15}{4}=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x\left(x+5\right)=0\\\left(x+\frac{5}{4}\right)^2=-\frac{15}{4}\left(vn\right)\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)
NN
0
Ta có : \(4\left(x-3\right)^2=9\left(2-3x\right)^2\)
\(\Leftrightarrow\left(2x-6\right)^2=\left(6-9x\right)^2\)
\(\Leftrightarrow\left(2x-6\right)^2-\left(6-9x\right)^2=0\)
\(\Leftrightarrow\left(3x-6-6+9x\right)\left(2x-6+6-9x\right)=0\)
\(\Leftrightarrow\left(12x-12\right)\cdot\left(-7x\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}12x-12=0\\-7x=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=0\end{cases}}\) ( thỏa mãn )
Vậy : phương trình đã cho có tập nghiệm \(S=\left\{0,1\right\}\)