\(x^2y+2x^2y+3x^2y+...+nx^2y=210x^2y\)

\(\Leftrightarrow x^2y\left(1+2+3+....+n\right)=210x^2y\)

\(\Leftrightarrow1+2+3+....+n=210\)

\(\Leftrightarrow\frac{n\left(n+1\right)}{2}=210\)

\(\Leftrightarrow n\left(n+1\right)=420=20.21\)

\(\Rightarrow n=20\)

Ta có : x²y + 2x²​y + 3x²​y + ......+ nx²​y = 210x²​y

<=> x²​y(1 + 2 + 3 + ...... + n) = 210x²​y

=> 1 + 2 + 3 + ...... + n = 210

Áp dụng công thức \(\frac{n\left(n+1\right)}{2}=210\)

Mà 210 = 20.21

Nên n = 20

(2x+1).(y-3)=15

* 2x+1=15                    * y-3=15

  2x=15-1                           x=15+3

  2x=14                               x=18

    x=14:2

    x=7

vậy x=7 hoặc x=18

\(\left(2x-1\right).\left(5-y\right)=15\)

\(\Rightarrow\)\(2x-1\inƯ\left(15\right)=\left\{1;3;5;15\right\}\)

        \(5-y\inƯ\left(15\right)=\left\{1;3;5;15\right\}\)

Ta có bảng sau :

Tự thay vào

x=12

y=18

đúng đó

1)

xy + x - 4y = 12

x + y(x - 4) = 12

y(x - 4) = 12 - x

\(y=\dfrac{-x+12}{x-4}\)

Vì \(x,y\inℕ\) nên

\(\left(-x+12\right)⋮\left(x-4\right)\)

\(\left(-x+12\right)-\left(x-4\right)⋮\left(x-4\right)\)

\(16⋮\left(x-4\right)\)

\(\left(x-4\right)\inƯ\left(16\right)\)

\(\left(x-4\right)\in\left\{1;-1;2;-2;4;-4;8;-8;16;-16\right\}\)

\(x\in\left\{5;3;6;2;8;0;12;-4;20;-12\right\}\)

\(y\in\left\{\dfrac{-5+12}{5-4};\dfrac{-3+12}{3-4};\dfrac{-6+12}{6-4};\dfrac{-2+12}{2-4};\dfrac{-8+12}{8-4};\dfrac{-0+12}{0-4};\dfrac{-12+12}{12-4};\dfrac{4+12}{-4-4};\dfrac{-20+12}{20-4};\dfrac{12+12}{-12-4}\right\}\)

\(y\in\left\{7;-9;3;-5;1;-3;0;-2;-\dfrac{1}{2};-\dfrac{7}{5}\right\}\)

\(\left(x;y\right)\in\left\{\left(5;7\right);\left(3;-9\right);\left(6;3\right);\left(2;-5\right);\left(8;1\right);\left(0;-3\right);\left(12;0\right);\left(-4;-2\right);\left(20;-\dfrac{1}{2}\right);\left(-12;-\dfrac{7}{5}\right)\right\}\)

Mà \(x,y\inℕ\) nên các giá trị cần tìm là \(\left(x;y\right)\in\left\{\left(5;7\right);\left(6;3\right);\left(8;1\right);\left(12;0\right)\right\}\)

2)

(2x + 3)(y - 2) = 15

\(\left(2x+3\right)\inƯ\left(15\right)\)

\(\left(2x+3\right)\in\left\{1;-1;3;-3;5;-5;15;-15\right\}\)

Ta lập bảng

Mà \(x,y\inℕ\) nên các giá trị cần tìm là \(\left(x;y\right)\in\left\{\left(0;7\right);\left(1;5\right);\left(6;3\right)\right\}\)

các thầy cô ơi giúp em vs ạ mai em phải nộp r ạ!!!

x=1;y=8

thanks các bạn nhìu nha