\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{2009}-1\right)\\ =\left(\dfrac{1}{2}-\dfrac{2}{2}\right)\left(\dfrac{1}{3}-\dfrac{3}{3}\right)...\left(\dfrac{1}{2009}-\dfrac{2009}{2009}\right)\\ =\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\dfrac{-2008}{2009}\\ =\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{2008}{2009}\\ =\dfrac{2\cdot3\cdot...\cdot2008}{\left(2\cdot3\cdot...\cdot2008\right)\cdot2009}\\ =\dfrac{1}{2009}\)

|x|=|y|

mà x>0; y<0

nên x=-y

2x+y=-2y+y=-y

\(\left|x\right|=\left|y\right|\) và \(x>0;y< 0\)

\(\Rightarrow y=-x\)

\(\Rightarrow2x\pm x=x\)

Vậy \(2x+y=x\)

\(\dfrac{6^{13}-3\cdot6^{12}+3^{13}}{9^5\left(4^6+1\right)}\)

\(=\dfrac{2^{13}\cdot3^{13}-2^{12}\cdot3^{13}+3^{13}}{3^{10}\left(2^{12}+1\right)}\)

\(=\dfrac{3^{12}\left(2^{13}-2^{12}+1\right)}{3^{10}\left(2^{12}+1\right)}=\dfrac{3^2\cdot\left[2^{12}\left(2-1\right)+1\right]}{2^{12}+1}\)

\(=\dfrac{9\left(2^{12}+1\right)}{2^{12}+1}\)

=9

Ý bạn là sao nhỉ???

Bn viết sai hoặc là viết thiếu câu hỏi r.

Chớ mik đọc hổng hỉu j hớt á

\(\dfrac{x+5}{97}+\dfrac{x+5}{98}+\dfrac{x+5}{99}=0\\ \Rightarrow\left(x+5\right).\left(\dfrac{1}{97}+\dfrac{1}{98}+\dfrac{1}{99}\right)=0\)
Vì \(\dfrac{1}{97}+\dfrac{1}{98}+\dfrac{1}{99}\ne0\) nên:
\(x+5=0\\ \Rightarrow x=-5\)
Vậy...

\(\dfrac{x+5}{97}+\dfrac{x+5}{98}+\dfrac{x+5}{99}=0\)

=>\(\left(x+5\right)\left(\dfrac{1}{97}+\dfrac{1}{98}+\dfrac{1}{99}\right)=0\)

=>x+5=0

=>x=-5

(3x-5)(2y+7)=100

=>(3x-5;2y+7)\(\in\){(1;100);(100;1);(-1;-100);(-100;-1);(2;50);(50;2);(-2;-50);(-50;-2);(4;25);(25;4);(-4;-25);(-25;-4);(5;20);(20;5);(-5;-20);(-20;-5);(10;10);(-10;-10)}

=>(3x;2y)\(\in\){(6;93);(105;-6);(4;-107);(-95;-8);(7;43);(55;-5);(3;-57);(-45;-9);(9;18);(30;-3);(1;-32);(-20;-11);(10;13);(25;-2);(0;-27);(-15;-12);(15;3);(-5;-17)}

=>(x;y)\(\in\){(2;93/2);(35;-3);(4/3;-107/2);(-95/3;-4);(7/3;43/2);(55/3;-5/2);(1;-57/2);(-15;-9/2);(3;9);(10;-3/2);(1/3;-16);(-20/3;-11/2);(10/3;13/2);(25/3;-1);(0;-27/2);(-5;-6);(5;3/2);(-5/3;-17/2)}

(3x - 5)(2y + 7) = 100

Ta có: 100 = 1 x 100 = 2 x 50 = 4 x 25

Do 2y + 7 là số lẻ nên 2y + 7 chỉ có thể = 1 hoặc 25

Trường hợp 1: 2y + 7 = 1

⇒ 2y = 1 - 7

⇒ 2y = -6

⇒ y = (-6) : 2

⇒ y = -3

Vậy 3x - 5 = 100

⇒ 3x = 100 + 5

⇒ 3x = 105

⇒ x = 105 : 3

⇒ x = 35

Trường hợp 2: 2y + 7 = 25

⇒ 2y = 25 - 7

⇒ 2y = 18

⇒ y = 18 : 2

⇒ y = 9

Vậy 3x - 5 = 4

⇒ 3x = 4 + 5

⇒ 3x = 9

⇒ x = 9 : 3

⇒ x = 3

Vậy (x; y) ϵ {(35; -3); (3; 9)}

|x-1|+|2x-2|+|3x-3|=12

=>\(\left|x-1\right|+2\left|x-1\right|+3\left|x-1\right|=12\)

=>\(6\left|x-1\right|=12\)

=>|x-1|=2

=>\(\left[{}\begin{matrix}x-1=2\\x-1=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)

cảm ơn

a: \(\widehat{MON}+\widehat{O_1}+45^0=180^0\)

=>\(\widehat{O_1}=180^0-90^0-45^0=45^0\)

Ta có: \(\widehat{O_1}=\widehat{MNO}\left(=45^0\right)\)

mà hai góc này là hai góc ở vị trí so le trong

nên OB//AM

b: Ta có: OB//AM

MA\(\perp\)AB

Do đó: OB\(\perp\)BA