Đáp án:
$\text{a) (x+3)³ - 3x² -x³ +9 = x - 8 }$
$\text{⇔ x³ + 27x + 9x² +27 -3x² -x³ +9 = x - 8 }$
$\text{⇔ x³ -x³ +9x² -3x² +27x -x +27 +9 +8=0 }$
$\text{⇔ 6x² +26x +44 =0 }$
$\text{⇔ (√6x)² + 2.√6x.$\dfrac{13\sqrt[]{6}}{6}$ + ($\dfrac{13\sqrt[]{6}}{6}$)² - ($\dfrac{13\sqrt[]{6}}{6}$)² +44 =0 }$
$\text{⇔ (√6x + $\dfrac{13\sqrt[]{6}}{6}$)² + $\dfrac{95}{6}$ =0 }$
$\text{Mà (√6x + $\dfrac{13\sqrt[]{6}}{6}$) ² ≥ 0 }$
$\text{⇒ (√6x + $\dfrac{13\sqrt[]{6}}{6}$)² + $\dfrac{95}{6}$ >0 ∀ x ∈ R }$
$\text{⇒ x vô nghiệm }$
$\text{Vậy x ∈ { ∅} }$
$\text{b)(x+3)(x-3) + 8x-2 =2x +1 }$
$\text{⇔ x² -9 + 8x -2 =2x +1 }$
$\text{⇔ x² +8x -2x -9-2-1 =0 }$
$\text{⇔ x² +6x -12 =0}$
$\text{⇔ x² +2.x.3+(3)² -(3)² -12 =0 }$
$\text{⇔ (x +3)² - 21 =0 }$
$\text{⇔ (x+3 - √21) (x+3+√21) =0 }$
$\text{⇔ \(\left[ \begin{array}{l}x+3 - √21=0\\x+3+√21=0\end{array} \right.\) }$
$\text{⇔\(\left[ \begin{array}{l}x=-3+ \sqrt21\\x=-3-\sqrt21\end{array} \right.\) }$
$\text{Vậy x ∈ { -3+ $\sqrt21$ ; -3 - $\sqrt{21}$ } }$
