1 reply to this topic

[hoaadc08]

Giải phương trình : 

$\sqrt{2x^{2}-x+3}+x^{2}-x=\sqrt{21x-17}$

[anh1999]

Giải phương trình : 

$\sqrt{2x^{2}-x+3}+x^{2}-x=\sqrt{21x-17}$

 dk $x\geq \frac{17}{21}$

ta có 

pt<=>$\sqrt{2x^2-x+3}-\sqrt{21x-17}+x^2-x=0$

<=>$\frac{(x-1)(2x-20)}{\sqrt{2x^2-x+3}+\sqrt{21x-17}}-x(x-1)$=0

<=>$(x-1)(\frac{x(\sqrt{2x^2-x+3}-3)+x(\sqrt{21x-17}-5)+10(x-2)}{\sqrt{2x^2-x+3}+\sqrt{21x-17}})=0$

<=>$(x-1)(x-2)(\frac{\frac{2x^2+3x}{\sqrt{2x^2-x+3}+3}+\frac{21x}{\sqrt{21x-17}+5}+10}{\sqrt{2x^2-x+3}+\sqrt{21x-17}})=0$

<=>x=1 hoặc x=2