NGUYỄN QUỐC PHƯƠNG hay đấy, nói dễ mak ko ghi đc lời giải hay sao??? có pải là ba hoa quá ko???

(x-2)(x+5)<0

=>x-2 và x+5 trái dấu

Mà x-2<x+5

=>\(\left\{{}\begin{matrix}x-2< 0\\x+5>0\end{matrix}\right.\)=>\(\left\{{}\begin{matrix}x< 2\\x>-5\end{matrix}\right.\)=>-5<x<2

=>x E {-4;-3;-2;-1;0;1}

\(\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{\dfrac{2}{3}-\dfrac{2}{7}-\dfrac{2}{13}}\cdot\dfrac{\dfrac{3}{4}-\dfrac{3}{16}-\dfrac{3}{64}-\dfrac{3}{264}}{1-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}}-\dfrac{11}{8}\)

\(=\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{2\left(\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}\right)}\cdot\dfrac{\dfrac{3}{4}\left(1-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}\right)}{1-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}}-\dfrac{11}{8}\)

\(=\dfrac{1}{2}\cdot\dfrac{3}{4}-\dfrac{11}{8}\)

\(=\dfrac{3}{8}-\dfrac{11}{8}\)

\(=1\)

Xét tích: a(b+m) = ab+am (1)

b(a+m)=ab+bm (2)

+) Nếu a<b => am < bm (3)

Từ (1),(2),(3) => a(b+m) < b(a+m) => \(\dfrac{a}{b}< \dfrac{a+m}{b+m}\)

+) Nếu a>b => am > bm (4)

Từ (1),(2),(4) => a(b+m) > b(a+m) => \(\dfrac{a}{b}>\dfrac{a+m}{b+m}\)

+) Nếu a=b => \(\dfrac{a}{b}=\dfrac{a+m}{b+m}\)

4*5=20

TICK NHÉ !!

rùi tick  cho tròn 130 nha mk gửi câu tl cho

Nếu a = 3k => a²+1=9k²+1 chia 3 dư 1

Nếu a = 3k+1 => a²+1=(3k+1)²+1=9k²+6k+1 chia 3 dư 1

Nếu a=3k+2 => a²+1=(3k+2)²+1=9k²+12k+5 chia 3 dư 2

Vậy...

Gọi mẫu số là x (x E Z)

Theo bài ra ta có: \(\dfrac{3}{5}< \dfrac{10}{x}< \dfrac{5}{6}\)

\(\Rightarrow\dfrac{30}{50}< \dfrac{30}{3x}< \dfrac{30}{36}\)

\(\Rightarrow36< 3x< 50\)

\(\Rightarrow x\in\left\{5;6;7;8;9;10;11;12;13;14;15;16\right\}\)

Vậy...

\(\Rightarrow\dfrac{x+y}{xy}=\dfrac{1}{2}\)

=> 2(x+y)=xy

=>2x+2y=xy

=>xy-2x-2y=0

=>x(y-2)-2y+4=0+4

=>x(y-2)-2(y-2)=4

=>(x-2)(y-2)=4

Ta có bảng:

Vậy các cặp (x;y) là (3;6);(1;-2);(4;4);(0;0);6;3);(-2;1)