Đặt : \(\dfrac{x}{5}=\dfrac{y}{3}=k\)

`=>x=5k,y=3k`

Ta có : \(x^2-y^2=4=>\left(5k\right)^2-\left(3k\right)^2=4\\ =>25k^2-9k^2=4\\ =>16k^2=4\\ =>k^2=\dfrac{1}{4}\\ =>k=\pm\dfrac{1}{2}\)

\(=>\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=\dfrac{3}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x=-\dfrac{5}{2}\\y=-\dfrac{3}{2}\end{matrix}\right.\end{matrix}\right.\)

\(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{575}\)

\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{23.25}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{23}-\frac{1}{25}\)

\(=\frac{1}{3}-\frac{1}{25}=\frac{22}{75}\)

*\(\frac{\left(\frac{3}{10}-\frac{4}{15}-\frac{7}{20}\right).\frac{5}{19}}{\left[\frac{1}{14}+\frac{1}{7}-\left(-\frac{3}{35}\right)\right].\frac{4}{3}}=\frac{\left(\frac{18}{60}-\frac{16}{60}-\frac{21}{60}\right).\frac{5}{19}}{\left(\frac{5}{70}+\frac{10}{70}+\frac{6}{70}\right).\frac{4}{3}}=\frac{\frac{-19}{60}.\frac{5}{19}}{\frac{21}{70}.\frac{4}{3}}=\frac{\frac{-1}{12}}{\frac{14}{35}}=-\frac{1}{12}.\frac{35}{14}=\frac{-35}{168}\)

*\(\frac{\left(1+2+3+...+100\right).\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(6,3.12-21.3,6\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)

=\(\frac{\left(1+2+3+...+100\right)\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(\frac{63}{10}.12-21.\frac{18}{5}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)

=\(\frac{\left(1+2+3+...+100\right)\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(\frac{378}{5}-\frac{378}{5}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)

=\(\frac{\left(1+2+3+...+100\right)\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).0}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}=0\)

A= 2( 1/15 + 1/35 + 1/63+ 1/99+1/143)

A= 2(1/3x5 +1/5x7 + 1/7x9 + 1/9x11 + 1/11x13)

A=2(1/3-1/5+1/5-1/+1/7-1/9+1/9-1/11+1/11-1/13)

A=2(1/3-1/13)

A=2x10/39

A=20/39

A = 2/15 + 2/35 + 2/63 + 2/99 + 2/143

A = 2/3x5 + 2/5x7 + 2/7x9 + 2/9x11 + 2/11x13

A = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13

A = 1/3 - 1/13

A = 12/13

A = 2/15 + 2/35 + 2/63 + 2/99 + 2/143

A = 2/3x5 + 2/5x7 + 2/7x9 + 2/9x11 + 2/11x13

A= 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13

A = 1/3 - 1/13

A = 10/39

\(2^3.x+2002^0.3=995-15\)

\(\Rightarrow8x+3=980\)

\(\Rightarrow8x=980-3=977\)

\(\Rightarrow x=977:8=\frac{977}{8}\)

**** đúng nka

a: =(8/27+19/27)+(4/15+11/15)=1+1=2

b: =(12/13+8/13+6/13)+(2/7+5/7)=2+1=3

d=-2 nhé bạn

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\)
\(=1-\frac{1}{9}=\frac{8}{9}\)

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\)( chỗ này tối giản nha )

\(=1-\frac{1}{9}\)

\(=\frac{8}{9}\)
~ Hok tốt ~

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}\)

\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\)

\(=1+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)-\frac{1}{9}\)

\(=1-\frac{1}{9}=\frac{8}{9}\)

~ Hok tốt ~

a) \(...\Rightarrow\left\{{}\begin{matrix}x-2=0\\y+3=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=2\\y=-3\end{matrix}\right.\)

b) \(...\Rightarrow|x-2|=|x+3|\Rightarrow\left[{}\begin{matrix}x-2=x+3\\x-2=-x-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}0x=5\\2x=-1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x\in\varnothing\\x=-\dfrac{1}{2}\end{matrix}\right.\)

\(\Rightarrow x=-\dfrac{1}{2}\)

c) \(|x-\dfrac{3}{4}|+|x+\dfrac{5}{4}|=1\)

\(\Rightarrow\left\{{}\begin{matrix}x-\dfrac{3}{4}\le0\\x+\dfrac{5}{4}\ge0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x\le\dfrac{3}{4}\\x\ge-\dfrac{5}{4}\end{matrix}\right.\)

\(\Rightarrow-\dfrac{5}{4}\le x\le\dfrac{3}{4}\)