\(\frac{3x-2}{8}=\frac{5y+6}{3}=\frac{3x-5y-8}{8-3}=\frac{3x-5y-8}{5}\)
\(+,3x=5y+8\Rightarrow\frac{5y+6}{8}=\frac{5y+6}{3}\Rightarrow y=-\frac{6}{5}\Rightarrow x=\frac{2}{3}\)
\(+,3x\ne5y+8\Rightarrow5=10x\Leftrightarrow x=\frac{1}{2}\Rightarrow\frac{-1}{16}=\frac{5y+6}{3}\Rightarrow....\)
\(xy+x+y+1=5\Leftrightarrow x\left(y+1\right)+\left(y+1\right)=5\Leftrightarrow\left(x+1\right)\left(y+1\right)=5\)
x;y nguyên nên đến đây dễ rồi
\(2.3^{x-2}+4.3^{x-2}=162\Rightarrow6.3^{x-2}=162\Leftrightarrow3^{x-2}=\frac{162}{6}=27\)
\(\Rightarrow3^{x-2}=27=3^3\)
\(\Rightarrow x-2=3\Leftrightarrow x=5\)
Áp dungjtc của dãy tỉ số bằng nhau :
\(\frac{5y+6}{3}=\frac{3x-2}{8}=\frac{3x-5y-8}{10x}=\frac{5y+6-3x+2+3x-5y-8}{3-8+10x}=\frac{0}{-5+10x}=0\)
\(=>\hept{\begin{cases}3x-2=0\\5y+6=0\end{cases}=>\hept{\begin{cases}3x=2\\5y=-6\end{cases}=>\hept{\begin{cases}x=\frac{2}{3}\\y=-\frac{6}{5}\end{cases}}}}\)
vậy...
b,\(xy+y+x=4\)
\(=>y.\left(x+1\right)+1.\left(x+1\right)=3\)
\(=>\left(y+1\right).\left(x+1\right)=3\)
Ta có bảng sau :
y+1 1 3 -1 -3
x+1 3 1 -3 -1
y 0 2 -2 -4
x 2 0 -4 -2
vậy ...
