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Câu 3:
a: \(\left(x+2\right)^2=x^2+4x+4\)
b: \(\left(x+3\right)^2=x^2+6x+9\)
c: \(\left(x-3\right)^2=x^2-6x+9\)
d: \(\left(x-7\right)^2=x^2-14x+49\)
e: \(x^2-6x+9=\left(x-3\right)^2\)
f: \(x^2-8x+16=\left(x-4\right)^2\)
g: \(=\left(x-10\right)\left(x+10\right)\)
h: \(=\left(x-11\right)\left(x+11\right)\)
a)
\(=\left(\dfrac{x}{x+3}-\dfrac{x^2+9}{\left(x-3\right)\left(x+3\right)}\right):\left(\dfrac{3x+1}{x\left(x-3\right)}-\dfrac{1}{x}\right)\)
\(=\left(\dfrac{x\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}-\dfrac{x^2+9}{\left(x-3\right)\left(x+3\right)}\right):\left(\dfrac{3x+1}{x\left(x-3\right)}-\dfrac{x-3}{x\left(x-3\right)}\right)\)
\(=\left(\dfrac{x^2-3x-x^2-9}{\left(x+3\right)\left(x-3\right)}\right):\left(\dfrac{3x+1-x+3}{x\left(x-3\right)}\right)\)
\(=\dfrac{-3\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}:\dfrac{2x+4}{x\left(x-3\right)}\)
\(=\dfrac{-3}{\left(x-3\right)}\cdot\dfrac{x\left(x-3\right)}{2x+4}\\ =\dfrac{-3x}{2x+4}\)
b)
với `x=-1/2` (tmđk) ta có
\(\dfrac{-3\cdot\left(\dfrac{-1}{2}\right)}{2\cdot\left(-\dfrac{1}{2}\right)+4}=\dfrac{1}{2}\)
c)
để P=x thì
\(\dfrac{-3x}{2x+4}=x\)
\(=>-3x=\left(2x+4\right)\cdot x\)
\(-3x=2x^2+4x\)
\(2x^2+4x+3x=0\)
\(2x^2+7x=0\)
\(x\left(2x+7\right)=0\)
\(=>\left[{}\begin{matrix}x=0\\2x+7=0\end{matrix}\right.=>\left[{}\begin{matrix}x=0\left(loại\right)\\x=-\dfrac{7}{2}\left(tm\right)\end{matrix}\right.\)
d)
mik ko bt lm=)
\(\Leftrightarrow2\left(x+1\right)^3=56\Leftrightarrow\left(x+1\right)^3=28\Leftrightarrow\)
\(15x^2y^5-10x^3y^4=5x^2y^4\left(3y-2x\right)\)
\(4x\left(x-2y\right)+7\left(2y-x\right)=4x\left(x-2y\right)-7\left(x-2y\right)=\left(x-2y\right)\left(4x-7\right)\)
\(5x^3+20x^2y+20xy^2=5x\left(x^2+4xy+4y^2\right)=5x\left(x+2y\right)^2\)
\(x^2-4y^2-2x+4y=\left(x-2y\right)\left(x+2y\right)-2\left(x-2y\right)=\left(x-2y\right)\left(x+2y-2\right)\)
Bài 2:
Ta có: \(3n^3+10n^2-5⋮3n+1\)
\(\Leftrightarrow3n^3+n^2+9n^2+3n-3n-1-4⋮3n+1\)
\(\Leftrightarrow3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)
\(\Leftrightarrow3n\in\left\{0;-3;3\right\}\)
hay \(n\in\left\{0;-1;1\right\}\)
\(=\dfrac{5(x+4)}{(x+4)(x-4)}+\dfrac{4(x-4)}{(x+4)(x-4)}-\dfrac{2x-24}{(x+4)(x-4)} \\=\dfrac{7x+28}{(x+4)(x-4)} \\=\dfrac{7(x+4)}{(x+4)(x-4)} \\=\dfrac{7}{x-4}\)
b: \(=\dfrac{5x+20+4x-16-2x+24}{\left(x-4\right)\left(x+4\right)}=\dfrac{7x+28}{\left(x-4\right)\left(x+4\right)}=\dfrac{7}{x-4}\)
giúp mình bài này với ạ,từng bước lun nhé,mình cảm ơn ạ
