\(A=x^2-10xy-11y^2\)

\(A=\left(x-5y\right)^2-25y^2-11y^2\)

\(A=\left(x-5y^2\right)-36y^2\)

\(A=\left(x-5y\right)^2-\left(6y\right)^2\)

\(A=\left(x-5y-6y\right)\left(x-5y+6y\right)\)

\(A=\left(x-11y\right)\left(x+y\right)\)

\(A=13\)hệ nghiệm ngyên quen thuộc

=> x,y

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

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

\(\Leftrightarrow x^2-1-y\left(x-1\right)+3=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)-y\left(x-1\right)=-3\)

\(\Leftrightarrow\left(x-1\right)\left(x+1-y\right)=-3\)

...

b ) \(3xy-5x-2y=3\)

\(\Leftrightarrow9xy-15x-6y=9\)

\(\Leftrightarrow9xy-15x-6y+10=19\)

\(\Leftrightarrow3y\left(3x-2\right)-5\left(3x-2\right)=19\)

\(\Leftrightarrow\left(3y-5\right)\left(3x-2\right)=19\)

...

c ) \(x^2-10xy-11y^2=13\)

\(\Leftrightarrow x^2-11xy+xy-11y^2=13\)

\(\Leftrightarrow x\left(x-11y\right)+y\left(x-11y\right)=13\)

\(\Leftrightarrow\left(x+y\right)\left(x-11y\right)=13\)

...

d ) \(xy-2=2x+3y\)

\(\Leftrightarrow xy-2-2x-3y=0\)

\(\Leftrightarrow y\left(x-3\right)-2\left(x-3\right)-8=0\)

\(\Leftrightarrow\left(y-2\right)\left(x-3\right)=8\)

...

e ) \(5xy+x+2y=7\)

\(\Leftrightarrow5xy+x+2y-7=0\)

\(\Leftrightarrow5x\left(y+\dfrac{1}{5}\right)+2\left(y+\dfrac{1}{5}\right)-\dfrac{37}{5}=0\)

\(\Leftrightarrow\left(5x+2\right)\left(y+\dfrac{1}{5}\right)=\dfrac{37}{5}\)

\(\Leftrightarrow\left(5x+2\right)\left(5y+1\right)=37\)

...

P/s : Vì bài dài nên việc tìm x , y ( lập bảng ) bạn tự làm nhé

Thanks

Hi , câu này mik trả lời rồi mà bạn :D

\(\frac{6}{7x}=\frac{9}{11y}=\frac{2}{3z}\) như thế ak

ta có:6/7x=9/11y=2/3z=k suy ra x=7/6k; y=11/9k;z=3/2 k

ta có: 7/6k+11/9k+3/2k=350

35/9k=350

k=350:35/9=90

x=90x7/6105

y=90x11/9=110

z=90x3/2=135

\(\Leftrightarrow4xy-4x-11y+121=121\)

\(\Leftrightarrow4x\left(y-1\right)-11\left(y-1\right)=121\)

\(\Leftrightarrow\left(4x-11\right)\left(y-1\right)=121\)

Pt ước số, chắc em tự giải nốt được