1) 2x2 + 7x - 9 = 0
\(\Leftrightarrow\) 2x2 - 2x + 9x - 9 = 0
\(\Leftrightarrow\) 2x(x - 1) + 9 (x - 1) = 0
\(\Leftrightarrow\) (x - 1)(2x + 9) = 0
\(\Leftrightarrow\) x - 1 = 0 hoặc 2x + 9 = 0
*x - 1 = 0
\(\Leftrightarrow\) x = 1
*2x + 9 = 0
\(\Leftrightarrow\) x = \(-\frac{9}{2}\)
Vậy S = {1 ; \(-\frac{9}{2}\)}.
2) x2 - 4x + 3 = 0
\(\Leftrightarrow\) x2 - x - 3x + 3 = 0
\(\Leftrightarrow\) x(x - 1) -3(x - 1) = 0
\(\Leftrightarrow\) (x - 1)(x - 3) = 0
\(\Leftrightarrow\) x - 1 = 0 hoặc x - 3 = 0
* x - 1 = 0
\(\Leftrightarrow\) x = 1
* x - 3 = 0
\(\Leftrightarrow\) x = 3.
Vậy S = {1; 3}.
3) x4 + x3 + x + 1 = 0
\(\Leftrightarrow\) x3(x + 1) + x + 1 = 0
\(\Leftrightarrow\) (x + 1)(x3 + 1) = 0
\(\Leftrightarrow\) x + 1 = 0 hoặc x3 + 1 = 0
*x + 1 = 0
\(\Leftrightarrow\) x = -1
*x3 + 1 = 0
\(\Leftrightarrow\) x3 = -1
\(\Leftrightarrow\) x = -1.
Vậy S = {-1}.
4) x4 - x2 + 2x + 2 = 0
\(\Leftrightarrow\) x2 (x2 - 1) + 2(x + 1) = 0
\(\Leftrightarrow\) x2 (x - 1)(x + 1) + 2(x + 1) = 0
\(\Leftrightarrow\) (x + 1)[x2(x - 1) + 2] = 0
\(\Leftrightarrow\) (x + 1)(x3 - x2 + 2) = 0
\(\Leftrightarrow\) x + 1 = 0 hoặc x3 - x2 + 2 = 0
*x + 1 = 0
\(\Leftrightarrow\) x = -1
*x3 - x2 + 2 = 0
\(\Leftrightarrow\) x3 + x2 - 2x2 + 2 = 0
\(\Leftrightarrow\) x2(x + 1) - 2(x2 - 1) = 0
\(\Leftrightarrow\) x2(x + 1) - 2(x - 1)(x + 1) = 0
\(\Leftrightarrow\) (x + 1)[x2 - 2(x - 1)] = 0
\(\Leftrightarrow\) (x + 1)(x2 - 2x + 2) = 0
\(\Leftrightarrow\) x + 1 = 0 hoặc x2 - 2x + 2 = 0
* x + 1 = 0
\(\Leftrightarrow\) x = -1
* x2 - 2x + 2 = 0
(x - 1)2 + 1 > 0 Với mọi x
Vậy S = {-1}.