this is lan . she live in Bao Loc city
she wears a blue dress
she is beautiful

1)
S1=(1+999)+(2+998)+...+(501+499)+500
S1=1000.(999-1)+500
S1=998 000 + 500
S1=998 500
 

a)
\(=10\sqrt{2}-3\sqrt{2}+\sqrt{2}=8\sqrt{2}\)
b)
\(=\dfrac{11\left(4+\sqrt{5}\right)}{\left(4-\sqrt{5}\right)\left(4+\sqrt{5}\right)}-\dfrac{3\left(\sqrt{5}-\sqrt{2}\right)}{\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}-\sqrt{2}\right)}\)
\(=\dfrac{11\left(4+\sqrt{5}\right)}{16-5}-\dfrac{3\left(\sqrt{5}-\sqrt{2}\right)}{5-2}\)
\(=4+\sqrt{5}-\sqrt{5}+3=7\)
c)
\(=\sqrt{b^2}.\sqrt{\left(b-1\right)^2}\left(b< 0\right)\)
\(=-b.\left(1-b\right)=-b+b^2\)

6,51.7=3.15.19
45,57=45,57

a)
\(\sqrt{\left(2x+1\right)^2}=3\)
TH1 x \(\ge\) -1/2
2x+1=3
2x=2
x=1
TH2 x< -12
1-2x=3
-2x=2
x=-1
 

\(=\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}=\sqrt{3-2\sqrt{5}+3}=\sqrt{9-2\sqrt{5}}\)

lộn
\(=2\sqrt{11}-7\)

\(=\sqrt{11}-3-4+\sqrt{11}=-7\)

\(A=\dfrac{3}{2}.\left(\dfrac{-2}{9}:\dfrac{1}{3}+\dfrac{4}{21}\right)-\dfrac{-3}{7}\)
\(A=\dfrac{3}{2}.\left(\dfrac{-2}{3}+\dfrac{4}{21}\right)+\dfrac{3}{7}\)
\(A=\dfrac{3}{2}.\dfrac{-10}{21}+\dfrac{3}{7}\)
A\(=-\dfrac{5}{7}+\dfrac{3}{7}=\dfrac{-2}{7}\)

a)
\(=\dfrac{1}{4}\left(\dfrac{2}{5}+\dfrac{3}{5}\right)=\dfrac{1}{4}.1=\dfrac{1}{4}\)
b)
\(=\dfrac{-5}{3}\left(\dfrac{2}{13}+\dfrac{11}{13}\right)=\dfrac{-5}{3}.1=\dfrac{-5}{3}\)
c)
\(=\dfrac{4}{25}+\dfrac{21}{25}.1-\dfrac{5}{24}:\dfrac{7}{12}\)
\(=\dfrac{4}{25}+\dfrac{21}{25}-\dfrac{5}{14}=1-\dfrac{5}{14}=\dfrac{9}{14}\)