Advertisements (Quảng cáo)
Bằng định thức, giải các hệ phương trình sau:
a)
\(\left\{ \matrix{
5x – 4y = 3 \hfill \cr
7x – 9y = 8 \hfill \cr} \right.\)
b)
\(\left\{ \matrix{
\sqrt 3 x + \sqrt 2 y = – 1 \hfill \cr
2\sqrt 2 x + \sqrt 3 y = 0 \hfill \cr} \right.\)
a) Ta có:
\(D = \left| \matrix{
5\,\,\,\, – 4 \hfill \cr
7\,\,\,\, – 9 \hfill \cr} \right| = – 45 + 28 = – 17\)
\({D_x} = \left| \matrix{
3\,\,\,\,\,\, – 4 \hfill \cr
8\,\,\,\,\,\, – 9 \hfill \cr} \right| = – 27 + 32 = 5\)
\({D_y} = \left| \matrix{
5\,\,\,\,\,\,\,3 \hfill \cr
7\,\,\,\,\,\,8 \hfill \cr} \right| = 40 – 21 = 19\)
Advertisements (Quảng cáo)
Hệ có nghiệm:
\(\left\{ \matrix{
x = {{{D_x}} \over D} = {{ – 5} \over {17}} \hfill \cr
y = {{{D_y}} \over D} = – {{19} \over {17}} \hfill \cr} \right.\)
b) Ta có:
\(D = \left| \matrix{
\sqrt 3 \,\,\,\,\,\,\,\sqrt 2 \hfill \cr
2\sqrt 2 \,\,\,\,\sqrt 3 \hfill \cr} \right| = 3 – 4 = – 1\)
\({D_x} = \left| \matrix{
– 1\,\,\,\,\,\,\sqrt 2 \hfill \cr
0\,\,\,\,\,\,\,\,\,\sqrt 3 \hfill \cr} \right| = – \sqrt 3 \)
\({D_y} = \left| \matrix{
\sqrt 3 \,\,\,\,\,\, – 1 \hfill \cr
2\sqrt 2 \,\,\,\,\,\,0 \hfill \cr} \right| = 2\sqrt 2 \)
Hệ có nghiệm duy nhất:
\(\left\{ \matrix{
x = {{{D_x}} \over D} = \sqrt 3 \hfill \cr
y = {{{D_y}} \over D} = – 2\sqrt 2 \hfill \cr} \right.\)