Question

Answer 1

Bài 6:

Thay x = -y vào R ta có:

\(R=2\cdot\left(-y\right)^2\cdot y-3y^2+2\cdot\left(-y\right)y^2-2y^2-1\\ =2y^3-3y^2-2y^3-2y^2-1\\ =\left(2y^3-2y^3\right)+\left(-3y^2-2y^2\right)-1\\ =-5y^2-1\)

Ta có: \(y^2\ge0\forall y\)

\(=>-5y^2\le0\forall y\\ =>R=-5y^2-1\le-1< 0\forall y\)

Vậy: ... 

Answer 2

Bài 6 :

\(R=2x^2y-3y^2+2xy^2-2y^2-1\)

\(R=2x^2y-5y^2+2xy^2-1\)

\(R=2\left(-y\right)^2y-5y^2+2\left(-y\right)y^2-1\) Vì \(x=-y\)

\(R=-2y^3-5y^2-2y^3-1\)

\(R=-2y^3-2y^3-5y^2-1\)

\(R=-4y^3-5y^2-1\)

mà \(-4y^3\le0,\forall y\in R\) ; \(-5y^2\le0,\forall y\in R\) ; \(-1< 0\)

\(\Rightarrow R=-4y^3-5y^2-1< 0,\forall x=-y\in R\left(dpcm\right)\)