Question

cmr khong co cac so x,y,x thoa man moi dang thuc sau: A = 2x^2 + y^2 - 2xy + x + 2 = 0

Answer 1

\(A=2x^2+y^2-2xy+x+2\)

\(A=\left(x^2-2xy+y^2\right)+\left[x^2+2.x.\frac{1}{2}+\left(\frac{1}{2}\right)^2\right]+\frac{7}{4}\)

\(A=\left(x-y\right)^2+\left(x+\frac{1}{2}\right)^2+\frac{7}{4}\)

Ta có: \(\hept{\begin{cases}\left(x-y\right)^2\ge0\forall x;y\\\left(x+\frac{1}{2}\right)^2\ge0\forall x\end{cases}}\Rightarrow\left(x-y\right)^2+\left(x+\frac{1}{2}\right)^2+\frac{7}{4}=A\ge\frac{7}{4}>0\forall x;y\)

Vậy không có các số tự nhiên thỏa mã đẳng thức \(A=2x^2+y^2-2xy+x+2=0\)