Question

Cho x,y thỏa mãn: x²+y²=2x-1.Tính giá trị biểu thức A=2x²⁰¹²+5y²⁰¹³

Answer 1

\(x^2+y^2=2x-1\Leftrightarrow x^2-\left(2x-1\right)+y^2=0\Leftrightarrow\left(x^2-2x+1\right)+y^2=0\Leftrightarrow\left(x-1\right)^2+y^2=0\) \(Mà:\left\{{}\begin{matrix}\left(x-1\right)^2\ge0\\y^2\ge0\end{matrix}\right.nên:\left\{{}\begin{matrix}\left(x-1\right)^2=0\\y^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-1=0\\y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=0\end{matrix}\right.\)

\(\Rightarrow A=2\)