a: \(\left(x+5\right)^2>=0\forall x\)

\(\left(2y-8\right)^2>=0\forall y\)

Do đó: \(\left(x+5\right)^2+\left(2y-8\right)^2>=0\forall x,y\)

Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x+5=0\\2y-8=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=-5\\y=4\end{matrix}\right.\)

b: \(\left(x+3\right)\left(2y-1\right)=5\)

=>\(\left(x+3\right)\left(2y-1\right)=1\cdot5=5\cdot1=\left(-1\right)\cdot\left(-5\right)=\left(-5\right)\cdot\left(-1\right)\)

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

=>\(\left(x,y\right)\in\left\{\left(-2;3\right);\left(2;1\right);\left(-4;-2\right);\left(-8;0\right)\right\}\)

nhanh dum mk vs mk dang can gap

\(xy^2-\left(x-2\right)\left(x^4+2x+1\right)=2y^2\)

\(\Rightarrow xy^2-2y^2-\left(x-2\right)\left(x^4+2x+1\right)=0\)

\(\Rightarrow y^2\left(x-2\right)-\left(x-2\right)\left(x^4+2x+1\right)=0\)

\(\Rightarrow\left(x-2\right)\left(y^2-x^4-2x-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\y^2-x^4-2x-1=0\end{matrix}\right.\)

Thay \(x=2\) vào \(y^2-x^4-2x-1=0\) ta có:

\(y^2-2^4-2\cdot2-1=0\)

\(\Rightarrow y^2-21=0\)

\(\Rightarrow y^2=21\)

\(\Rightarrow\left[{}\begin{matrix}y=\sqrt{21}\\y=-\sqrt{21}\end{matrix}\right.\)

Vậy (x;y) thỏa mãn là: \(\left(2;\sqrt{21}\right);\left(2;-\sqrt{21}\right)\)

lý thuyết đầy đủ các phuong phap giai phuong trinh nghiem nguyen

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

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

=> x + y + 2 = xy

x + y - xy = -2

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

x.( 1 - y ) - ( 1 - y ) = -2 - 1

( 1 - y ).( x - 1 ) = -3

- ( y - 1 ).( x - 1) = -3

=> ( y - 1 ).( x - 1 ) = 3

=> ( y - 1 ) ; ( x - 1 ) \(\in\) Ư( 3 ) = { 1; -1; 3; -3 }

Ta có bảng sau

Vậy ( x ; y ) \(\in\) { ( 4 ; 2 ); ( -2 ; 0 ); ( 2; 4 ); ( 0; -2 ) }

5x + 2y - xy = 16

=> 5x +  y(2 - x) = 16

=> 5x - 10 - y(x - 2) = 6

=> 5(x - 2) - y(x - 2) = 6

=> (5 - y)(x - 2) = 6

ta có bảng :

5x + 2y - xy = 16
5x + 2y - xy - 10 = 6
(5x - 10) + (2y - xy) = 6
5(x - 2) - y(x - 2) = 6
(x - 2)(5 - y) = 6
Vì x,y là các số nguyên => x - 2,5 - y là các ước nguyên của 6
Ta có bảng sau:
 

Chúc bạn học tốt!