$a) 3x^2 - 2x - 5 = 0$
$<=> 3x^2 + 3x -5x -5=0$
$<=> 3x(x+1) - 5(x+1) = 0$
$<=> (x+1)(3x-5) = 0$
<=> \(\left[ \begin{array}{l}x+1=0\\3x-5=0\end{array} \right.\)
<=> \(\left[ \begin{array}{l}x=-1\\x=5/3\end{array} \right.\)
.
$b) -7x^2 + 9x -2 = 0$
$<=> 7x^2 - 9x + 2 =0$
$<=> 7x^2 -2x - 7x + 2 =0$
$<=> x(7x-2) -(7x-2) = 0$
$<=> (7x-2)(x-1)=0$
<=> \(\left[ \begin{array}{l}7x-2=0\\x-1=0\end{array} \right.\)
<=> \(\left[ \begin{array}{l}x=2/7\\x=1\end{array} \right.\)
.
$c) 1/2x^2 - 3x + 2 = 0$
Đen ta: $9 - 4.2.1/2 = 5$
=> x1= $\frac{3-√5}{1}$ =3-√5
x2= $\frac{3+√5}{1}$ =3+√5
.
$d) (5+ √2)x^2 + (5-√2)x - 10=0$
Đen ta: $(5-√2)² - 4(5+ √2).(-10)$
$= 25 - 10√2 + 2 +200 + 40√2$
$= 30√2 + 227$
=> x1= $\frac{√2-5+\sqrt[]{30√2+227}}{2(5+√2)}$ = 1
x2= $\frac{√2-5-\sqrt[]{30√2+227}}{2(5+√2)}$
