Question

Giải các phương trình :

a)2x²+2xy+y²+9=6x-/y+3/

b)(2x²+x-213)²+4(x²-5x-2012)²=4(2x²+x-213)(x²-5x-2012)

Answer 1

a/\(\Leftrightarrow\left(x^2+2xy+y^2\right)+\left(x^2-6x+9\right)=-\left|y+3\right|\)

\(\Leftrightarrow\left(x+y\right)^2+\left(x-3\right)^2=-\left|y+3\right|\)

Ta thấy VT\(\ge0,VP\le0\Rightarrow\)Dấu bằng xảy ra khi 2 vế bằng 0

\(\Rightarrow\left\{{}\begin{matrix}y=-3\\x=3\end{matrix}\right.\)

Answer 2

\(\Leftrightarrow\left(2x^2+x-2013\right)^2-4\left(2x^2+x-2013\right)\left(x^2-5x-2012\right)+4\left(x^2-5x-2012\right)^2=0\)

\(\Leftrightarrow\left(2x^2+x-2013-2\left(x^2-5x-2012\right)\right)^2=0\)

\(\Leftrightarrow11x+2011=0\Rightarrow x=-\frac{2011}{11}\)