a) \(a< -a\Leftrightarrow2a< 0\Leftrightarrow a< 0\)

b) \(a>-a\Leftrightarrow2a>0\Leftrightarrow a>0\)

c)\(a=-a\Leftrightarrow2a=0\Leftrightarrow a=0\)

a. a < -a <=> a < 0

b. a > -a <=> a > 0

c. a = -a <=> a = 0

\(\hept{\begin{cases}\left(x+\frac{2019}{2020}\right)^{100}\ge0\\\left(y-\frac{9}{11}\right)^{200}\ge0\end{cases}}\Rightarrow\hept{\begin{cases}x+\frac{2019}{2020}=0\\y-\frac{9}{11}\ge0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{-2019}{2020}\\y=\frac{9}{11}\end{cases}}\)

Ta có : \(\left[x+\frac{2019}{2020}\right]^{100}\ge0\forall x\)

\(\left[y-\frac{9}{11}\right]^{200}\ge0\forall y\)

\(\Leftrightarrow\left[x+\frac{2019}{2020}\right]^{100}+\left[y-\frac{9}{11}\right]^{200}\ge0\forall x,y\)

Dấu " = " xảy ra khi : \(\hept{\begin{cases}x+\frac{2019}{2020}=0\\y-\frac{9}{11}=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-\frac{2019}{2020}\\y=\frac{9}{11}\end{cases}}\)

\(\left|x-\frac{2}{3}\right|+\left|y+\frac{5}{9}\right|=0\)

Vì \(\left|x-\frac{2}{3}\right|\ge0\)và \(\left|y+\frac{5}{9}\right|\ge0\)nên \(\left|x-\frac{2}{3}\right|+\left|y+\frac{5}{9}\right|\ge0\)

(Dấu "="\(\Leftrightarrow\)\(\left|x-\frac{2}{3}\right|=0\)và \(\left|y+\frac{5}{9}\right|=0\))

\(\Leftrightarrow\hept{\begin{cases}x=\frac{2}{3}\\y=\frac{-5}{9}\end{cases}}\)

vì \(\left|x-\frac{2}{3}\right|>0\)hoặc =0 ;\(\left|y+\frac{5}{9}\right|>0\)hoặc =o

mà\(\left|x-\frac{2}{3}\right|+\left|y+\frac{5}{9}\right|=0\)

nên |x-2/3| =0 và |y+5/9|=0

\(\Rightarrow\hept{\begin{cases}x-\frac{2}{3}=0\\y+\frac{5}{9}=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=\frac{2}{3}\\y=\frac{-5}{9}\end{cases}}}\)

Mỗi nhóm "HỌC SINH GIỎI LỚP 5" có 14 chữ cái.

Ta có : 2014 ÷ 14 = 143 ( dư 12 )

Vậy chữ cái thứ 2014 là chữ L.

Cbht

\(15:\left\{150:\left[95-\left(3^3+3^2.2\right)\right]\right\}\)

\(=15:\left\{150:\left[95-\left(27+9.2\right)\right]\right\}\)

\(=15:\left\{150:\left[95-\left(27+18\right)\right]\right\}\)

\(=15:\left\{150:\left[95-45\right]\right\}\)

\(=15:\left\{150:50\right\}\)

\(=15:3\)

\(=5\)

A = 1 + 3 + 3² + 3³ + ... + 3²⁰¹⁵

3A = 3 + 3² + 3³ + 3⁴ + ... + 3²⁰¹⁶

3A - A = ( 3 + 3² + 3³ + 3⁴ + ... + 3²⁰¹⁶ ) - ( 1 + 3 + 3² + 3³ + ... + 3²⁰¹⁵ )

2A = 3²⁰¹⁶ - 1

A = ( 3²⁰¹⁶ - 1 ) : 2 < B = 3²⁰²⁰- 1 : 2 => A < B

1)    \(\frac{2}{3}x+\frac{3}{4}\left(x-5\right)=-\frac{5}{6}\)

      \(\frac{2}{3}x+\frac{3}{4}x-\frac{15}{4}=-\frac{5}{6}\)

       \(\frac{17}{12}x=-\frac{5}{6}+-\frac{15}{4}=-\frac{55}{12}\)

   \(x=-\frac{55}{12}:\frac{17}{12}=-\frac{55}{17}\)

53(15+172-84)=53.103=53.(100+3)=5300+159=5459

15.53+53.172-53.84=5459