a) \(y\times15+y\times13=560\times45\)

\(y\times\left(15+13\right)=25200\)

\(y\times28=25200\)

\(y=25200:28\)

\(y=900\)

b) \(y\times345-y\times44-y=123600\)

\(y\times\left(345-44-1\right)=123600\)

\(y\times300=123600\)

\(y=123600:300\)

\(y=412\)

x=-1;y=1

x=-1;y=-1

x=-5;y=-1

x=-5;y=1

a)(x+3)^2-3=y^2

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

y=+-1

x={-5, -1}

\(x^2+6x+6=y^2\\ \left(x+3\right)^2-y^2=3\\ \left(x-y+3\right)\left(x+y+3\right)=3\)

Vì x,y nguyên nên x-y+3 và x+y+3 nguyên

=>\(\left(x-y+3\right)\left(x+y+3\right)=-1\cdot3=1\cdot-3=3\cdot-1=-3\cdot1\)

TH1:

\(\hept{\begin{cases}x-y+3=-1\\x+y+3=3\end{cases}=>\hept{\begin{cases}x=-2\\y=2\end{cases}}}\)

TH2:

\(\hept{\begin{cases}x-y+3=1\\x+y+3=-3\end{cases}=>\hept{\begin{cases}x=-4\\y=-2\end{cases}}}\)

TH3:

\(\hept{\begin{cases}x-y+3=3\\x+y+3=-1\end{cases}=>\hept{\begin{cases}x=-2\\y=-2\end{cases}}}\)

TH4:

\(\hept{\begin{cases}x-y+3=-3\\x+y+3=1\end{cases}=>\hept{\begin{cases}x=-4\\y=2\end{cases}}}\)

1000-345+345:y= 655 +345 :5

3x²+5y²=345

=> 3x²+5y²=300+45

=> 3x²+5y²=3.100+5.9

=> 3x²+5y²=3.10²+5.3²

=> x=10; y=3.

x =-10 ; y = -3

Hoặc x = 10 ; y = 3