Question

bài12 ; tìm đa thức A biết

1) A - (xy + x² - y² ) = x² + y²                      2) ( 6x² - 3xy² ) + A = x² + y² - 2xy²

3) A + ( x² + y² ) = 5x² + 3y² - xy             4) A + ( 5x² - 2xy ) = 6x² + 9xy - y²

5) A + (3x²y - 2xy³) = 2x²y - 4xy³            6) A + ( x² - 2y² ) = x² - y² + 3y² - 1

 

 

 

Answer 1

\(1,A-\left(xy+x^2-y^2\right)=x^2+y^2\)
\(\Rightarrow A=x^2+y^2+\left(xy+x^2-y^2\right)\)
\(\Rightarrow A=2x^2+xy\)
\(2,\left(6x^2-3xy^2\right)+A=x^2+y^2-2xy^2\)
\(\Rightarrow A=x^2+y^2-2xy^2-\left(6x^2-3xy^2\right)\)
\(\Rightarrow A=x^2+y^2-3xy^2-6x^2+3xy^2\)
\(\Rightarrow A=-5x^2+y^2+xy^2\)
\(3,A+\left(x^2+y^2\right)=5x^2+3y^2-xy\)
\(\Rightarrow A=5x^2+3y^2-xy-\left(x^2+y^2\right)\)
\(\Rightarrow A=5x^2+3y^2-xy-x^2-y^2\)
\(\Rightarrow A=4x^2+2y^2-xy\)
\(4,A+\left(5x^2-2xy\right)=6x^2+9xy-y^2\)
\(\Rightarrow A=6x^2+9xy-y^2-\left(5x^2-2xy\right)\)
\(\Rightarrow A=6x^2+9xy-y^2-5x^2+2xy\)
\(\Rightarrow A=x^2-y^2+11xy\)
\(5,A+\left(3x^2y-2xy^3\right)=2x^2y-4xy^3\)
\(\Rightarrow A=2x^2y-4xy^3-\left(3x^2y-2xy^3\right)\)
\(\Rightarrow A=2x^2y-4xy^3-3x^2y+2xy^3\)
\(\Rightarrow A=-x^2y-2xy^3\)
\(6,A+\left(x^2-2y^2\right)=x^2-y^2+3y^2-1\)
\(\Rightarrow A=x^2+2y^2-1-\left(x^2-2y^2\right)\)
\(\Rightarrow A=x^2+2y^2-1-x^2+2y^2\)
\(\Rightarrow A=4y^2-1\)