x,y nguyên không bạn

\(B=\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\\ =\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}+\dfrac{1}{9\times10}\\ =\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\\ =\dfrac{1}{4}-\dfrac{1}{10}\\ =\dfrac{10}{40}-\dfrac{4}{40}\\ =\dfrac{6}{40}\\ =\dfrac{3}{20}\)

Cửa hàng còn lại số kg gạo là:
`1850-480-520=850`(kg)

Đáp số: 850 kg

\(a,M=\dfrac{1}{12}x^7y^{10}+\left(\dfrac{1}{7}x^5y^7\right)\left(-\dfrac{7}{3}x^2y^3\right)=\dfrac{1}{12}x^7y^{10}-\dfrac{1}{3}x^7y^{10}\)

b, Thay x=-1, y=-1 vào M ta có:
\(\dfrac{1}{12}x^7y^{10}-\dfrac{1}{3}x^7y^{10}=\dfrac{1}{12}.\left(-1\right)^7.\left(-1\right)^{10}-\dfrac{1}{3}.\left(-1\right)^7.\left(-1\right)^{10}=\dfrac{1}{12}.\left(-1\right).1-\dfrac{1}{3}.\left(-1\right).1=\dfrac{-1}{12}+\dfrac{1}{3}=\dfrac{1}{4}\)

\(\left(x+\dfrac{1}{5}\right)^2+\dfrac{13}{25}=\dfrac{17}{25}\\ \Leftrightarrow\left(x+\dfrac{1}{5}\right)^2=\dfrac{4}{25}\\ \Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{5}=\dfrac{2}{5}\\x+\dfrac{1}{5}=-\dfrac{2}{5}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{5}\\x=-\dfrac{3}{5}\end{matrix}\right.\)

\(a,4+3x=25-4x\\ \Leftrightarrow7x=21\\ \Leftrightarrow x=3\\ b,\left(x-1\right)^2+\left(x-1\right)\left(x+3\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-1+x+3\right)=0\\ \Leftrightarrow\left(x-1\right)\left(2x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\2x+2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)

c, ĐKXĐ:\(x\ne-1,x\ne2\)

\(\dfrac{1}{x+1}+\dfrac{3}{x-2}=\dfrac{9}{\left(x+1\right)\left(x-2\right)}\\ \Leftrightarrow\dfrac{x-2}{\left(x+1\right)\left(x-2\right)}+\dfrac{3\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}-\dfrac{9}{\left(x+1\right)\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{x-2+3x+3-9}{\left(x+1\right)\left(x-2\right)}=0\\ \Rightarrow4x-8=0\\ \Leftrightarrow x=2\left(ktm\right)\)

C

\(\left(x+1\right)\left(x^2-x+1\right)-2x=x\left(x-1\right)\left(x+1\right)\\ \Leftrightarrow x^3+1-2x=x\left(x^2-1\right)\\ \Leftrightarrow x^3+1-2x=x^3-x\\ \Leftrightarrow1-x=0\\ \Leftrightarrow x=1\)