Bổ sung đề : Tìm x,y nguyên :\(\left(x-2\right)\left(y+1\right)=-2\)

Vì \(-2=\left(-2\right).1=2.\left(-1\right)\)nên ta có :

+, \(\orbr{\begin{cases}x-2=-2\\y+1=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\y=0\end{cases}}\)

+, \(\orbr{\begin{cases}x-2=1\\y+1=-2\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\y=-3\end{cases}}\)

+, \(\orbr{\begin{cases}x-2=2\\y+1=-1\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\y=-2\end{cases}}\)

+, \(\orbr{\begin{cases}x-2=-1\\y+1=2\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\y=1\end{cases}}\)

\(A=\dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{50^2}\)

\(A< \dfrac{1}{1^2}+\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{49.50}\)

\(A< 1+\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\)

\(A< 1+1-\dfrac{1}{50}=2-\dfrac{1}{50}< 2\) (đpcm)

`Answer:`

Bài 1:

a. \(-415.25-8=-10375-8=-10383\)

b. \(\left(-154\right).\left(-1625\right)=250250\)

c. \(-54.135=-7290\)

d. \(178:414=\frac{178}{414}=\frac{89}{207}\)

e. \(-209.513=-107217\)

f. \(-48:-245=\frac{48}{245}\)

Bài 2:

a. \(x+13=-73\Leftrightarrow x=-73-13\Leftrightarrow x=-86\)

b. \(x-113=-79\Leftrightarrow x=-79+113\Leftrightarrow x=34\)

c. \(2x+12=-53\Leftrightarrow2x=-53-12\Leftrightarrow2x=-65\Leftrightarrow x=-32,5\)

d. \(-59:x=169\Leftrightarrow x=-59:169\Leftrightarrow x=-\frac{59}{169}\)

Bài 3:

a. \(65+[3+\left(-15\right)]=65+3-15=\left(65-15\right)+3=53\)

b. \(\left(-57\right).211+\left(-57\right).911+157=\left(-57\right).\left(211+911\right)+157=-63954+157=-63797\)

c. \(819+421+25+1721+\left(-2719\right)=\left(819+1721\right)+\left(421-2719\right)+25=2540-2298+25=267\)

\(\left(\frac{1}{2}.x+\frac{1}{4}\right).\left(2.x-\frac{1}{3}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}.x+\frac{1}{4}=0\\2.x-\frac{1}{3}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}x=-\frac{1}{4}\\2x=\frac{1}{3}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=\frac{1}{6}\end{cases}}\)

Vậy x = -1/2 hoặc x = 1/6