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a) \(\left(x+6\right)^2-x\left(x+9\right)=0\)
\(\Leftrightarrow\)\(x^2+12x+36-x^2-9x=0\)
\(\Leftrightarrow\)\(3x+36=0\)
\(\Leftrightarrow\)\(x=-12\)
Vậy...
b) \(6x\left(2x+5\right)-\left(3x+4\right)\left(4x-3\right)=9\)
\(\Leftrightarrow\)\(12x^2+30x-12x^2-7x+12=9\)
\(\Leftrightarrow\)\(23x+12=9\)
\(\Leftrightarrow\)\(x=-\frac{3}{23}\)
Vậy
c) \(2x\left(8x+3\right)-\left(4x+1\right)=13\)
\(\Leftrightarrow\)\(16x^2+6x-4x-1=13\)
\(\Leftrightarrow\)\(16x^2+2x-14=0\)
\(\Leftrightarrow\)\(8x^2+x-7=0\)
\(\Leftrightarrow\)\(\left(x+1\right)\left(8x-7\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=-1\\x=\frac{7}{8}\end{cases}}\)
Vậy
d) \(\left(x-4\right)^2-x\left(x+4\right)=0\)
\(\Leftrightarrow\)\(x^2-8x+16-x^2-4x=0\)
\(\Leftrightarrow\)\(-12x+16=0\)
\(\Leftrightarrow\)\(x=\frac{4}{3}\)
Vậy
e) \(\left(x-2\right)^2-\left(2x+3\right)\left(x-2\right)=0\)
\(\Leftrightarrow\)\(x^2-4x+4-2x^2+x+6=0\)
\(\Leftrightarrow\)\(-x^2-3x+10=0\)
\(\Leftrightarrow\)\(\left(2-x\right)\left(x+5\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=2\\x=-5\end{cases}}\)
Vậy
một đòn bẫy dài một mét .đặt ở đâu để có thể dùng 3600n có thể nâng tảng đá nặng 120kg?
a) (x2-6xy+9y2):(3y-x)
= (x-3y)2:(3y-x)
=(3y-x)2:(3y-x)
= 3y-x
b) (8x3-1):(4x2+2x+1)
=[(2x)3-1]:(4x2+2x+1)
= (2x-1)(4x2+2x+1):(4x2+2x+1)
= 2x-1
c) (4x4-9):(2x2-3)
=(2x2-3)(2x2+3):(2x2-3)
=2x2+3
d) (8x3-27):(4x2+6x+9)
=(2x-3)(4x2+6x+9):(4x2+6x+9)
=2x-3
a) \(\dfrac{2x-2y}{x^2-2xy+y^2}=\dfrac{2\left(x-y\right)}{\left(x-y\right)^2}=\dfrac{2}{x-y}\)
b) \(\dfrac{2-2a}{a^3-1}=-\dfrac{2-2a}{1-a^3}=-\dfrac{2\left(1-a\right)}{\left(1-a\right)\left(1+a+a^2\right)}=\dfrac{-2}{\left(1+a+a^2\right)}\)
c) \(\dfrac{x^2-6x+9}{x^2-8x+15}\)
\(=\dfrac{x^2-2.x.3+3^2}{x^2-3x-5x+15}\)
\(=\dfrac{\left(x-3\right)^2}{\left(x^2-3x\right)-\left(5x-15\right)}\)
\(=\dfrac{\left(x-3\right)^2}{x\left(x-3\right)-5\left(x-3\right)}\)
\(=\dfrac{\left(x-3\right)^2}{\left(x-3\right)\left(x-5\right)}\)
\(=\dfrac{x-3}{x-5}\)
d) \(\dfrac{x^4-2x^3}{2x^4-x^3}\)
\(=\dfrac{x^3\left(x-2\right)}{x^3\left(2x-1\right)}\)
\(=\dfrac{x-2}{2x-1}\)
b: Ta có: \(\left(x-3\right)^3-\left(x+2\right)\left(x^2-2x+4\right)+9\left(x+2\right)^2\)
\(=x^3-9x^2+27x-27-x^3-8+9x^2+36x+36\)
\(=53x+1\)