Giải phương trình: $x^{4}\sqrt{x+3}=2x^{4}-2011x+2011$
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Posted 14-05-2017 - 21:57
NTMFlashNo1
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Giải phương trình: $x^{4}\sqrt{x+3}=2x^{4}-2011x+2011$
$x^{4}\sqrt{x+3}=2x^{4}-2011x+2011\\\Leftrightarrow x^{4}\left ( \sqrt{x+3}-2 \right )+2011\left ( x-1 \right )=0\\\Leftrightarrow x^{4}\frac{\left ( x+3 \right )-4}{\sqrt{x+3}+2}+2011\left ( x-1 \right )=0\\\Leftrightarrow \left ( x-1 \right )\left ( \frac{x^{4}}{\sqrt{x+3}+2}+2011 \right )=0\\\Leftrightarrow x=1$
Vậy $\boxed{\text{x=1}}$
Edited by NTMFlashNo1, 14-05-2017 - 21:57.
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$\boxed{\text{Nguyễn Trực-TT-Kim Bài secondary school}}$
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