Đáp án:
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`a,`
`I = x (y^2 - xy ) + y (x^2y - xy + x)`
`↔ I = xy^2 - x^2y + x^2y^2- xy^2 + xy`
`↔ I = (xy^2 - xy^2) - x^2y + x^2y^2 + xy`
`↔ I = -x^2y + x^2y^2 + xy`
Thay \(\left\{ \begin{array}{l}x=-3\\y=\dfrac{-1}{3}\end{array} \right.\) vào `I` ta được :
`↔ I = -(-3)^2 . (-1/3) + (-3)^2 . (-1/3)^2 + (-3) . (-1/3)`
`↔ I = -9 . (-1/3) + 9 . 1/9 + 1`
`↔ I = 3 + 1 + 1`
`↔I = 4 + 1`
`↔ I = 5`
Vậy `I=5` khi `x=-3,y=(-1)/3`
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`b,`
`K = x^2 (y^2 - xy^2 + 1) - (x^3 + x^2 + 1) y^2`
`↔ K = x^2y^2 - x^3y^2 + x^2 - (x^3y^2 + x^2y^2 + y^2)`
`↔ K = x^2y^2 - x^3y^2 + x^2 - x^3y^2 - x^2y^2 - y^2`
`↔ K = (x^2y^2 - x^2y^2) + (-x^3y^2 - x^3y^2) + x^2 - y^2`
`↔ K = -2x^3y^2 + x^2-y^2`
Thay \(\left\{ \begin{array}{l}x=0,5\\y=\dfrac{-1}{2}\end{array} \right.\) vào `K` ta được :
`↔ K = -2 . (0,5)^3 . (-1/2)^2 + (0,5)^2 - (-1/2)^2`
`↔ K = -2 . 1/8 . 1/4 + 1/4 - 1/4`
`↔ K = -1/4 . 1/4 + 1/4 - 1/4`
`↔ K = -1/16 + (1/4 - 1/4)`
`↔ K =-1/16`
Vậy `K=-1/16` khi `x=0,5; y=(-1)/2`
