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ko có đáp án nhé . mk nói thật luôn . nếu sai bạn đừng k nhé !
\(\left(x+1\right)^2-3\left(x+1\right)=\left(x+1\right)\left(x+1-3\right)=\left(x+1\right)\left(x-2\right)\)
\(2x\left(x-2\right)-\left(x-2\right)^2=\left(x-2\right)\left[2x-\left(x-2\right)\right]=\left(x-2\right)\left(2x-x+2\right)=\left(x-2\right)\left(x+2\right)\)
\(4x^2-20xy+25y^2=\left(2x\right)^2-2.2x.5y+\left(5y\right)^2=\left(2x-5y\right)^2\)
\(x^2+3x-x-3=x\left(x+3\right)-\left(x+3\right)=\left(x-1\right)\left(x+3\right)\)
\(x^2-xy+x-y=x\left(x-y\right)+\left(x-y\right)=\left(x-y\right)\left(x+1\right)\)
\(2y\left(x+2\right)-3x-6=2y\left(x+2\right)-3\left(x+2\right)=\left(x+2\right)\left(2y-3\right)\)
a) với a = -2 ta được phương trình:
3.[(-2) - 2].x + 2.(-2).(x - 1) = 4.(-2) + 3
<=> 3.(-4x) - 4.(x - 1) = (-8) + 3
<=> -12x - 4(x - 1) = -5
<=> -12x - 4x + 4 = -5
<=> -16x + 4 = -5
<=> -16x = -5 - 4
<=> -16x = -9
<=> x = 9/16
b) để x = 1, ta có:
3.(a - 2).1 + 2a(1 - 1) = 4a + 3
<=> 3(a - 2) + 0 = 4a + 3
<=> 3a - 6 = 4a + 3
<=> 3a - 6 - 4a = 3
<=> -a - 6 = 3
<=> -a = 3 + 6
<=> a = -9
Có: \(x^3-y^3=-3xy\left(y-x\right)\)
\(\Leftrightarrow x^3-y^3=-3xy^2+3x^2y\)
\(\Leftrightarrow x^3-3x^2y+3xy^2-y^3=0\)
\(\Leftrightarrow\left(x-y\right)^3=0\)
\(\Leftrightarrow x-y=0\Leftrightarrow x=y\)
Khi đó bt A trở thành:
\(A=\left(2x-y\right)\left(y-2x\right)\left(y-y\right)^2=\left(2x-y\right)\left(y-2x\right)\cdot0=0\)
a, (1-x)(5x+3)= (3x-8)(1-x)
<=> (1-x) (5x+3) - (3x-8)(1-x) =0 <=> (1-x) (2x+11) = 0
\(\Leftrightarrow\left[{}\begin{matrix}1-x=0\\2x+11=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{11}{2}\end{matrix}\right.\)
Vậy.........
b, (x-3)(x+4)-2(3x-2)=(x-4)^2
<=> 3x = 24<=> x=8
Vậy .......
c,x^2+ x^3+x+1=0
<=> x^2 (x+1) +(x+1) =0 <=> (x^2 +1)(x+1) =0
<=> x+1 =0 => x=-1
Vậy.......
d, \(\dfrac{x-3}{x+3}-\dfrac{2}{x-3}=\dfrac{3x+1}{9-x^2}\)
\(\Leftrightarrow x^2-6x+9-2x-6=-3x-1\)
\(\Leftrightarrow x^2-5x+4=0\Leftrightarrow\left(x+4\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=1\end{matrix}\right.\)
Vậy...........
Nếu \(x-2\ge0\Rightarrow x\ge2\Rightarrow\left|x-2\right|=x-2\)
Ta có phương trình
\(x^2-6\left(x-2\right)-4=0\)
\(\Rightarrow x^2-6x+12-4=0\)
\(\Rightarrow x^2-6x+8=0\)
\(\Rightarrow x^2-2x-4x+8=0\)
\(\Rightarrow x\left(x-2\right)-4\left(x-2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x-4\right)=0\)
\(\Rightarrow x-2=0\) hoặc \(x-4=0\)
\(\left(+\right)x-2=0\Rightarrow x=2\) (tm)
\(\left(+\right)x-4=0\Rightarrow x=4\) (tm)
Nếu \(x-2<0\Rightarrow x<2\Rightarrow\left|x-2\right|=-\left(x-2\right)=2-x\)
Ta có phương trình
\(x^2-6\left(2-x\right)-4=0\)
\(\Rightarrow x^2-12+6x-4=0\)
\(\Rightarrow x^2+6x-16=0\)
\(\Rightarrow x^2-2x+8x-16=0\)
\(\Rightarrow x\left(x-2\right)+8\left(x-2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+8\right)=0\)
\(\Rightarrow x-2=0\) hoặc \(x+8=0\)
\(\left(+\right)x-2=0\Rightarrow x=2\) (không tm)
\(\left(+\right)x+8=0\Rightarrow x=-8\left(tm\right)\)
Vậy phương trình có tập nghiệm \(S=\left\{-8;2;4\right\}\)
Taco:VD:2.3.4.5>24=>x<0
x=-2=>tổng=0
Vayx=-1
\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)=24\)
\(\Leftrightarrow\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)=0\)