Giải phương trình căn bậc hai 4x^2 + 5x + 1 - 2 căn bậc hai x^2 - x + 1 = 3 - 9x

Trả lời

$\sqrt{4x^2+5x+1}-2\sqrt{x^2-x+1}=3-9x (4x^2+5x+1\ge 0;x^2-x+1\ge 0)$

$\Rightarrow \left(\sqrt{4x^2+5x+1}-2\sqrt{x^2-x+1}\right)\left(\sqrt{4x^2+5x+1}+2\sqrt{x^2-x+1}\right)=\left(3-9x\right)\left(\sqrt{4x^2+5x+1}+2\sqrt{x^2-x+1}\right)$

$\Rightarrow \left(9x-3\right)=\left(3-9x\right)\left(\sqrt{4x^2+5x+1}+2\sqrt{x^2-x+1}\right)\iff \left[\begin{array}{l}\sqrt{4x^2+5x+1}+2\sqrt{x^2-x+1}=-1(lo¹i)\\ 9x-3=0\end{array}\right.$

$\Rightarrow$9x - 3 = 0 $\iff$x = $\frac{1}{3}$ (thoả mãn điều kiện)