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5:
=10x^3*1/2xy-2/5y*1/2xy+1/2z*1/2xy
=5x^3y-1/5xy^2+1/4xyz
6: =x^2y*4xy+x^2y*3y-5x*x^2y
=4x^3y^2+3x^2y^2-5x^3y
7: =-4/3xy*3x^2y+4/3xy*6xy-4/3xy*9x
=-4x^3y^2+8x^2y^2-12x^2y
\(\left|x+\dfrac{1}{7}\right|-\dfrac{2}{3}=0\)
\(\Rightarrow\left|x+\dfrac{1}{7}\right|=0+\dfrac{2}{3}\\ \Rightarrow\left|x+\dfrac{1}{7}\right|=\dfrac{2}{3}\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{7}=\dfrac{2}{3}\\x+\dfrac{1}{7}=-\dfrac{2}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}-\dfrac{1}{7}\\x=-\dfrac{2}{3}-\dfrac{1}{7}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{11}{21}\\x=-\dfrac{17}{21}\end{matrix}\right.\)
a: =>2x^3-2x^2+2x-x^2+x-1+3x^2-2x^3=2
=>3x-1=2
=>x=1
b: \(\Leftrightarrow\left(3x-6\right)\left(-4x+1\right)+4\left(3x^2+7x+2\right)=24\)
=>\(-12x^2+3x+24x-6+12x^2+28x+8=28\)
=>55x+2=28
=>55x=26
=>x=26/55
c: \(\Leftrightarrow\left(x^2+3x+2\right)\left(x+3\right)-x^3-8x^2-16x=6\)
=>\(x^3+3x^2+3x^2+9x+2x+6-x^3-8x^2-16x=6\)
=>-2x^2-5x=0
=>x=0 hoặc x=-5/2
d: =>x^3+2x^2+4x+x^2+2x+4-x^3-3x^2+8=0
=>6x+12=0
=>x=-2
Bài 2:
\(\dfrac{1}{2}:\dfrac{5}{4}=x:\dfrac{10}{3}\Leftrightarrow\dfrac{1}{2}.\dfrac{4}{5}=\dfrac{3}{10}x\Leftrightarrow\dfrac{3}{10}x=\dfrac{2}{5}\Leftrightarrow x=\dfrac{2}{5}:\dfrac{3}{10}=\dfrac{4}{3}\)
Bài 3:
Áp dụng t/c dtsbn:
\(\dfrac{x}{4}=\dfrac{y}{12}=\dfrac{x+y}{4+12}=\dfrac{48}{16}=3\)
\(\Rightarrow\left\{{}\begin{matrix}x=3.4=12\\y=3.12=36\end{matrix}\right.\)
Bài 3:
theo đề bài ta có:
\(\left\{{}\begin{matrix}2a-3b=0\\5b-7c=0\\3a-7b+5c=30\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=42\\b=28\\c=20\end{matrix}\right.\)
Bài 4:
Đặt \(\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{z}{6}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=4k\\y=5k\\z=6k\end{matrix}\right.\)
Ta có: \(x^2-2y^2+z^2=18\)
\(\Leftrightarrow16k^2-50k^2+36k^2=18\)
\(\Leftrightarrow k^2=9\)
Trường hợp 1: k=3
\(\Leftrightarrow\left\{{}\begin{matrix}x=4k=4\cdot3=12\\y=5k=5\cdot3=15\\z=6k=6\cdot3=18\end{matrix}\right.\)
Trường hợp 2: k=-3
\(\Leftrightarrow\left\{{}\begin{matrix}x=4k=-3\cdot4=-12\\y=5k=-3\cdot5=-15\\z=6k=-3\cdot6=-18\end{matrix}\right.\)