Đáp án:
$a, S =$ {$\frac{√37 - 3}{2} ; \frac{-√37 - 3}{2}$}
$b, S =${$2;3$}
Giải thích các bước giải:
$a, (x + 1)(2x - 3) = (x - 2)²$
$→ 2x² - x - 3 = x² - 4x + 4$
$→ 2x² - x - 3 - x² + 4x - 4 = 0$
$→ x²+ 3x - 7 = 0 $
$→ (x² + 3x + \frac{9}{4}) - \frac{37}{4} = 0$
$→ (x² + 2.x.\frac{3}{2} + \frac{9}{4}) = \frac{37}{4}$
$→ (x + \frac{3}{2})² = (± \frac{√37}{2})$
$→\left[ \begin{array}{l}x+ \frac{3}{2} = \frac{√37}{2}\\x+ \frac{3}{2} = \frac{-√37}{2}\end{array} \right.$
$→\left[ \begin{array}{l}x=\frac{√37-3}{2}\\x=\frac{-√37 - 3}{2}\end{array} \right.$
$Vậy$ $S=${$\frac{√37 - 3}{2} ;\frac{-√37-3}{2}$}
$b, x² - 4 - 5(x - 2)² = 0$
$→ (x - 2)(x+2) - 5(x-2)² = 0 $
$→(x - 2)[x + 2 - 5(x - 2)]=0$
$→(x - 2)(x + 2 - 5x +10)=0$
$→ (x - 2)(- 4x + 12)=0$
$→\left[ \begin{array}{l}x-2=0\\-4x+12=0\end{array} \right.$
$→\left[ \begin{array}{l}x=2\\x=3\end{array} \right.$
$Vậy$ $S=${$2;3$}
