`x^2y^2 − 16xy + 99 = 9x^2 + 36y^2 + 13x + 26y`
`->x^2y^2+20xy-36xy+100-1=9x^2+36y^2+13x+26y`
`->x^2y^2+20xy+100=9x^2+36y^2+13x+26y+36xy+1`
`->(x^2y^2+10)^2=(9x^2+36xy+36y^2)+13x+26y+1`
`->(xy+10)^2=(3x+6y)^2+13(x+2y)+1`
`->(xy+10)^2=9(x+2y)^2+13(x+2y)+1`
Đặt `{(x+2y=a(a>0)),(xy+10=b(b>10)):}`
`->b^2-1=9a^2+13a`
`↔9a^2+6a. 13/6+169/36-169/36=b^2-1`
`↔(3a+13/6)^2-b^2=133/36`
`↔(18a+13)^2-36b^2=133`
`↔(18a-6b+13)(18a+6b+13)=133(1)`
Ta có : `a,b>0->18a+6b+13>18a-6b+13>0`
Lại có : `133=19.7`
`->(1)↔`\(\left[ \begin{array}{l}\left \{ {{18a+6b+13=133} \atop {18a-6b+13=1}} \right. \\\left \{ {{18a+6b+13=19} \atop {18a-6b+13=7}} \right. \end{array} \right.\)
`↔`\(\left[ \begin{array}{l}\left \{ {{18a+6b=120} \atop {18a-6b=-12}} \right. \\\left \{ {{18a+6b=32} \atop {18a-6b=-6}} \right. \end{array} \right.\)
`↔`\(\left[ \begin{array}{l}\left \{ {{12b=132} \atop {3a-b=-2}} \right. \\\left \{ {{12b=38} \atop {3a-b=-1}} \right. \end{array} \right.\)
`↔`\(\left[ \begin{array}{l}\left \{ {{b=11} \atop {a=3}} \right. \\\left \{ {{b=\frac{19}{6}(KTM)} \atop {b=-\frac{25}{18}(KTM)}} \right. \end{array} \right.\)
`->``{(x+2y=3),(xy+10=11):}`
`↔``{(x=3-2y),(xy=1):}`
`↔``{(x=3-2y),(2y^2-3y+1=0):}`
`↔``{(x=3-2y),(2y-1=0),(y-1=0):}`
`↔``{(x=1),(y=1):}`
Vậy `x,y={1;1}`
