ĐK:\(x\ge-2010\)
\(x^2+\sqrt{x+2010}=2010\)
\(\Leftrightarrow x^2=2010-\sqrt{x+2010}\)
\(\Leftrightarrow x^2+x+\dfrac{1}{4}=x+2010-2\sqrt{x+2010}\dfrac{1}{2}+\dfrac{1}{4}\)
\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\left(\sqrt{x+2010}-\dfrac{1}{2}\right)^2\)
\(\Leftrightarrow x+\dfrac{1}{2}=\sqrt{x+2010}-\dfrac{1}{2}\)
ĐK:\(x\ge\dfrac{1}{2}\)
=>\(x^2+2x+1=x+2010\)
\(\Leftrightarrow x^2+x-2009=0\)
Giải phương trình này ra x=\(\left\{\dfrac{-1+3\sqrt{893}}{2}\right\}\)
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