giúp đỡ ạ :)
3x = 5x = 10z và x-2y-z=15
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\(\dfrac{1}{2}\left(6x-2y\right)\left(3x+y\right)=\dfrac{1}{2}.2\left(3x-y\right)\left(3x+y\right)=9x^2-y^2\)
\(\left(\dfrac{2}{3}z-\dfrac{2}{5}x\right)\left(\dfrac{1}{3}z+\dfrac{1}{5}x\right).\dfrac{1}{2}=\left(\dfrac{1}{3}z-\dfrac{1}{5}x\right)\left(\dfrac{1}{3}z+\dfrac{1}{5}z\right).2.\dfrac{1}{2}=\dfrac{1}{9}z^2-\dfrac{1}{25}x^2\)
\(\left(5y-3x\right).\dfrac{1}{4}\left(12x+20y\right)=\left(5y-3x\right)\left(5y+3x\right).4.\dfrac{1}{4}=25y^2-9x^2\)
\(\left(\dfrac{3}{4}y-\dfrac{1}{2}x\right)\left(x+\dfrac{3}{2}y\right)=\left(\dfrac{3}{2}y-x\right)\left(\dfrac{3}{2}y+x\right)=\dfrac{9}{4}y^2-x^2\)
\(\left(a+b+c\right)\left(a+b+c\right)=\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ac\)
\(\left(x-y+z\right)\left(x+y-z\right)=x^2-\left(y-z\right)^2=x^2-y^2-z^2+2yz\)
\(3x=5y=10z\Leftrightarrow\dfrac{x}{\dfrac{1}{3}}=\dfrac{y}{\dfrac{1}{5}}=\dfrac{z}{\dfrac{1}{10}}\)
\(\Rightarrow\dfrac{x}{\dfrac{1}{3}}=\dfrac{2y}{\dfrac{2}{5}}=\dfrac{z}{\dfrac{1}{10}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{\dfrac{1}{3}}=\dfrac{2y}{\dfrac{2}{5}}=\dfrac{z}{\dfrac{1}{10}}=\dfrac{x-2y-z}{\dfrac{1}{3}-\dfrac{2}{5}-\dfrac{1}{10}}=\dfrac{15}{-\dfrac{1}{6}}=-90\)
\(\Rightarrow\left\{{}\begin{matrix}x=-90.\dfrac{1}{3}=-30\\y=-90.\dfrac{1}{5}=-18\\z=-90.\dfrac{1}{10}=-9\end{matrix}\right.\)
3x=5x=10z cơ mà