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1) \(3x\left(x-1\right)+5\left(x-1\right)\)
\(=\left(x-1\right)\left(3x+5\right)\)
2) \(4x(x-2y)-8y(2y-x)\)
\(=4x\left(x-2y\right)+8y\left(x-2y\right)\)
\(=\left(4x+8y\right)\left(x-2y\right)\)
\(=4\left(x+2y\right)\left(x-2y\right)\)
3) \(a^2\left(x-1\right)+b^2\left(1-x\right)\)
\(=a^2\left(x-1\right)-b^2\left(x-1\right)\)
\(=\left(a^2-b^2\right)\left(x-1\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(x-1\right)\)
4) \(3x\left(x-a\right)+4a\left(a-x\right)\)
\(=3x\left(x-a\right)-4a\left(x-a\right)\)
\(=\left(x-a\right)\left(3x-4a\right)\)
5) \(5x\left(x-y\right)^2+10y^2\left(y-x\right)^2\)
\(=5x\left(x-y\right)^2+10y^2\left(x-y\right)^2\)
\(=\left(5x+10y^2\right)\left(x-y\right)^2\)
\(=5\left(x+2y^2\right)\left(x-y\right)^2\)
6) \(3x\left(x-3\right)^2+9\left(3-x\right)^2\)
\(=3x\left(x-3\right)^2+9\left(x-3\right)^2\)
\(=\left(3x+9\right)\left(x-3\right)^2\)
\(=3\left(x+3\right)\left(x-3\right)^2\)
7) \(x\left(m-a\right)^2-y\left(a-m\right)^2\)
\(=x\left(a-m\right)^2-y\left(a-m\right)^2\)
\(=\left(x-y\right)\left(a-m\right)^2\)
8) \(6y^2\left(x-1\right)^2+9y\left(1-x\right)^2\)
\(=6y^2\left(x-1\right)^2+9y\left(x-1\right)^2\)
\(=\left(6y^2+9x\right)\left(x-1\right)^2\)
\(=3\left(2y^2+3x\right)\left(x-1\right)^2\)
#Ayumu
\(3,\\ a,=a^2+2a+1-a^2+2a-1-3a^2+3=-3a^2+4a+3\\ b,=\left(m^3-m+1-m^2+3\right)^2=\left(m^3-m^2-m+4\right)^2\\ 4,\\ a,\Leftrightarrow25x^2+10x+1-25x^2+9=3\\ \Leftrightarrow10x=-7\Leftrightarrow x=-\dfrac{7}{10}\\ b,\Leftrightarrow-9x^2+30x-25+9x^2+18x+9=30\\ \Leftrightarrow48x=46\Leftrightarrow x=\dfrac{23}{24}\\ c,\Leftrightarrow x^2+8x+16-x^2+1=16\\ \Leftrightarrow8x=-1\Leftrightarrow x=-\dfrac{1}{8}\)
b, pt \(\Leftrightarrow\)mx - 2=0
Nếu m=0 pt\(\Leftrightarrow\) -2=0 (vô lí)\(\Rightarrow\)m=2(loại)
Nếu m\(\ne\)0 pt có nghiệm x=\(\dfrac{2}{m}\)
1) Biến đổi A, ta được:
\(A=\frac{x-2+7}{x-2}=1+\frac{7}{x-2}\)
Do đó:
\(A< 1\Rightarrow1+\frac{7}{x-2}< 1\Rightarrow\frac{7}{x-2}< 0\left(1\right)\)
Mà 7>0 nên:
\(\left(1\right)\Rightarrow x-2< 0\Rightarrow x< 2\)
2)
+) Biến đổi B, ta được:
\(B=\frac{3\left(x-2\right)+2x^2-x-19-x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\\ =\frac{3x-6+2x^2-x-19-x^2-2x}{\left(x-2\right)\left(x+2\right)}=\frac{x^2-25}{x^2-4}\left(đpcm\right)\)
+) Từ 1) và 2), ta suy ra:
\(P=\frac{B}{A}=\frac{\frac{x+5}{x-2}}{\frac{\left(x-5\right)\left(x+5\right)}{\left(x-2\right)\left(x+2\right)}}=\frac{1}{\frac{x-5}{x+2}}=\frac{x+2}{x-5}\)
3) Biến đổi P, ta được:
\(P=\frac{x-5+3}{x-5}=1+\frac{3}{x-5}\)
P nguyên khi và chỉ khi \(\frac{3}{x-5}\) nguyên, hay \(x-5\inƯ\left(3\right)\)
Ta có bảng:
| x-5 | -3 | -1 | 1 | 3 |
| x | 2 | 4 | 6 | 8 |
Vậy ta có 4 giá trị của x trên thoả mãn đề bài.
Chúc bạn học tốt nha
\(a,\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow8x+16-5x^2-10x+4\left(x^2-x-2\right)+2x^2-8=0\)
\(\Leftrightarrow8x+16-5x^2-10x+4x^2-4x-8+2x^2-8=0\)
\(\Leftrightarrow x^2-6x=0\)
\(\Leftrightarrow x\left(x-6\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)
Vậy pt có tập nghiệm \(S=\left\{0,6\right\}\)
\(b,4\left(x-1\right)\left(x+5\right)-\left(x+2\right)\left(x+5\right)=3\left(x-1\right)\left(x+2\right)\)
\(\Leftrightarrow4\left(x^2+4x-5\right)-x^2-7x-10-3\left(x^2+x-2\right)=0\)
\(\Leftrightarrow4x^2+16x-20-x^2-7x-10-3x^2-3x+6=0\)
\(\Leftrightarrow6x-24=0\)
\(\Leftrightarrow x=4\)
Vậy pt có nghiệm x = 4
a)(8-5x)(x+2)+4(x-2)(x+1)+2(x-2)(x+2)=0
8x-5x2+16-10x+4(x2-2x+x-2)+2(x2-4)=0
8x-5x2+16-10x+4x2-8x+4x-8+2x2-8=0
(8-10-8+4) x+(-5+4+2)x2+(16-8-8)=0
-6x+x2=0
x(-6+x)
TH1:x=0
TH2:-6+x=0
x=6
➞KL:x∈{0;6}
a: =>(x-6)(x+2)=0
=>x=6 hoặc x=-2
b: \(\Leftrightarrow25x^2+10x+1-25x^2+9=30\)
=>10x=20
hay x=2
c: =>x3-1-x3+4x=5
=>4x=6
hay x=3/2
a: =(6x)^2-(3x-2)^2
=(6x-3x+2)(6x+3x-2)
=(9x-2)(3x+2)
d: \(=\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\)
\(=4x\cdot\left[x^2+2x+1+x^2-2x+1\right]\)
=8x(x^2+1)
e: =(4x)^2-2*4x*3y+(3y)^2
=(4x-3y)^2
f: \(=-\left(\dfrac{1}{4}x^4-2\cdot\dfrac{1}{2}x^2\cdot2y^3+4y^6\right)\)
\(=-\left(\dfrac{1}{2}x^2-2y^3\right)^2\)
g: =(4x)^3+1^3
=(4x+1)(16x^2-4x+1)
k: =x^3(27x^3-8)
=x^3(3x-2)(9x^2+6x+4)
l: =(x^3-y^3)(x^3+y^3)
=(x-y)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)
Bạn tham khảo nhé