Bài làm
Ta có: P = x3 + x2y - 2x2 - xy - y2 + 3y + x + 2017
P = x3 + x2y - 2x2 - xy - y2 + 2y + y + x + 2017
P = ( x3 + x2y − 2x2 ) − ( xy + y2 − 2y ) + ( x + y − 2 ) + 2019
P = x2( x + y − 2 ) − y( x + y − 2 ) + ( x + y − 2 ) + 2019
Mà x + y = 2 => x + y - 2 = 0
Thay x + y - 2 = 0 và đa thức P, ta được:
P = x2 . 0 - y . 0 + 0 + 2019
P = 0 - 0 + 0 + 2019
P = 2019
Vậy P = 2019 tại x + y = 2
# Học tốt #
\(P=x^3+x^2y-2x^2-xy-y^2+3y+x+2017\)
\(P=\left(x^3+x^2y-2x^2\right)+\left(-xy-y^2+2y\right)+\left(x+y-2\right)+2019\)
\(P=x^2\left(x+y-2\right)-y\left(x+y-2\right)+\left(x+y-2\right)+2019\)
\(P=\left(x^2-y+1\right)\left(x+y-2\right)+2019\)
\(P=0+2019=2019\)
Ta có
\(P=x^3+x^2y-2x^2-xy-y^2+3y+x+2017\)
\(\Leftrightarrow x^3+x^2y-2x^2-xy-y^2+2y+y+x+2017\)
\(\Leftrightarrow\left(x^3+x^2y-2x^2\right)-\left(xy+y^2-2y\right)+\left(x+y-2\right)+2019\)
\(\Leftrightarrow x^2\cdot\left(x+y-2\right)-y\cdot\left(x+y-2\right)+\left(x+y-2\right)+2019\)
Ta có \(x+y=2\Rightarrow x+y-2=0\)
\(\Rightarrow P=2019\)
