Question

giải phương trình:

(2x²+x-2013)²+4(x²-5x-2012)²=4(2x²+2-2013)(x²-5x-2012)

Answer 1

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

\(\Leftrightarrow\left(2x^2+x-2013-2x^2+10x+4024\right)^2=0\)

\(\Leftrightarrow\left(11x+2011\right)^2=0\)

\(\Leftrightarrow x+2011=0\)

\(\Leftrightarrow11x=-2011\)

\(\Leftrightarrow x=\dfrac{2011}{11}.\)

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