\(3x^2y-7y=5x^2-84\)

=>\(9x^2y-21y=15x^2-252\)

=> \(3x^2\left(3y-5\right)-7\left(3y-5\right)=-217\)

=> \(\left(3y-5\right)\left(3x^2-7\right)=\left(-7\right).31=7\left(-31\right)=1\left(-217\right)=217\left(-1\right)\)

Đến đây bạn tự lập bảng ra xét nhé

\(\frac{-2}{x}=\frac{y}{3}\)

\(\Rightarrow-2\times3=x\times y\)

\(\Rightarrow-6=x\times y\)

\(\Leftrightarrow-6=-2\times3=3\times-2=-3\times2=2\times-3\)

vì\(x< 0< y\)

\(\Rightarrow x=-2;y=3\) hoặc\(x=-3;y=2\)

nên \(xy=2.\left(-3\right)=-2.3=-1.6=-6.1\)

Vậy các cặp giá trị \(\left(x,y\right)\)tìm được là\(\left(2:-3\right);\left(-3;2\right);\left(1;-6\right);\left(-6;1\right)\)

                                                          \(\left(-2;3\right);\left(3;-2\right);\left(-1;6\right);\left(6;-1\right)\)

Ta có: \(S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{9^2}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}.\)

Mà\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\)

\(=1-\frac{1}{9}=\frac{8}{9}\)

\(\Rightarrow S< \frac{8}{9}\)

Và \(S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{9^2}>\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{9.10}\)

Mà \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)

\(=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)

\(\Rightarrow S>\frac{2}{5}\)

Vậy: \(\frac{2}{5}< S< \frac{8}{9}\)

1)

a) x - 4/3 = 2 1/3                            b) 4/7 - 1/7x =13/14

x - 4/3 = 7/3                                   1/7x       = 4/7 - 13/14

x         = 7/3 + 4/3                          1/7x       = 8/14 - 13/14

x         = 11/3                                  1/7x       = -5/14

Vậy x = 11/3                                     Vậy x = -5/14

\(\frac{4}{7}-\frac{1}{7}x=\frac{13}{14}\)

\(\frac{4}{7}-\frac{1}{7}x=\frac{13}{14}+\frac{4}{7}=\frac{13}{14}+\frac{8}{14}\)

          \(\frac{1}{7}x=\frac{21}{14}\)

               \(x=\frac{21}{14}:\frac{1}{7}=\frac{21}{14}\times\frac{7}{1}\)

               \(x=\frac{147}{14}\)

In spite of she was sick, she did the test very well

k cho mình nha!

Although she was sick, she did the test very well.

C1: =>In spite of her sickness, she did the test very well.

C2: => In spite of being sick, she did the test very well.

\(Để\frac{n+1}{n^2+1}\in Z\)

\(\Rightarrow n+1⋮n^2+1\)

\(\Rightarrow\left(n+1\right)\left(n-1\right)⋮n^2+1\)

\(\Rightarrow n^2-1⋮n^2+1\)

\(\Rightarrow\left(n^2+1\right)-2⋮n^2+1\)

\(\Rightarrow n^2+1\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)

\(\Rightarrow n^2\in\left\{-3;-2;0;1\right\}\)

Vì n thuộc N

\(\Rightarrow n=1\)

1. what's your favorite programme

2. aren't suppose to spend too much time watching TV as it is not good for them

3. because he loves animal

4. of watching cartoons

5. We shouldn't throw old clothes away as it is not a good thing to do