Question

[Lizy]

giải pt

`(2x^2 +x-2016)^2 +4(x^2 -3x-1000)^2 = 4(2x^2 +x-2016)(x^2 -3x-1000)`

Answer 1

[Tô Mì]

Đặt: \(\left\{{}\begin{matrix}a=2x^2+x-2016\\b=x^2-3x-1000\end{matrix}\right.\). Phương trình trở thành:

\(a^2+4b^2=4ab\)

\(\Leftrightarrow a^2-4ab+4b^2=0\)

\(\Leftrightarrow\left(a-2b\right)^2=0\Leftrightarrow a=2b\)

\(\Rightarrow2x^2+x-2016=2\left(x^2-3x-1000\right)\)

\(\Leftrightarrow7x=16\Leftrightarrow x=\dfrac{16}{7}\)

Vậy: \(x=\dfrac{16}{7}\)