Giải các hệ phương trình sau bằng phương pháp thế:
a) \(\left\{{}\begin{matrix}x\sqrt{2}-y\sqrt{3}=1\\x+y\sqrt{3}=\sqrt{2}\end{matrix}\right.; \)
b) \(\left\{{}\begin{matrix}x-2\sqrt{2}y=\sqrt{5}\\x\sqrt{2}+y=1-\sqrt{10}\end{matrix}\right.; \)
c) \(\left\{{}\begin{matrix}(\sqrt{2}-1)x-y=\sqrt{2}\\x+(\sqrt{2}+1)y=1\end{matrix}\right.. \)
a)![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D%20x%5Csqrt%7B2%7D-%20y%20%5Csqrt%7B3%7D%3D1%20%26%20%26%20%5C%5C%20x%20+%20y%5Csqrt%7B3%7D%20%3D%20%5Csqrt%7B2%7D%26%20%26%20%5Cend%7Bmatrix%7D%5Cright.)
Từ phương trình (2) ⇔ x = √2 - y√3 (3)
Thế (3) vào (1): ( √2 - y√3)√2 - y√3 = 1
⇔ √3y(√2 + 1) = 1 ⇔ y =
= ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Csqrt%7B2%7D-1%7D%7B%5Csqrt%7B3%7D%7D)
Từ đó x = √2 -
. √3 = 1.
Vậy có nghiệm (x; y) = (1;
)
b)![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D%20x%20-%202%5Csqrt%7B2%7D%20y%20%3D%20%5Csqrt%7B5%7D%26%20%26%20%5C%5C%20x%5Csqrt%7B2%7D%20+%20y%20%3D%201%20-%20%5Csqrt%7B10%7D%26%20%26%20%5Cend%7Bmatrix%7D%5Cright.)
Từ phương trình (2) ⇔ y = 1 - √10 - x√2 (3)
Thế (3) vào (1): x - 2√2(1 - √10 - x√2) = √5
⇔ 5x = 2√2 - 3√5 ⇔ x =![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7B2%5Csqrt%7B2%7D-3%5Csqrt%7B5%7D%7D%7B5%7D)
Từ đó y = 1 - √10 -
. √2 = ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7B1%20-%202%5Csqrt%7B10%7D%7D%7B5%7D)
Vậy hệ có nghiệm (x; y) =
;
c)![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D%20%28%5Csqrt%7B2%7D-%201%29x%20-%20y%20%3D%20%5Csqrt%7B2%7D%26%20%26%20%5C%5C%20x%20+%20%28%5Csqrt%7B2%7D+%201%29y%20%3D%201%26%20%26%20%5Cend%7Bmatrix%7D%5Cright.)
Từ phương trình (2) ⇔ x = 1 - (√2 + 1)y (3)
Thế (3) vào (1): (√2 - 1)[1 - (√2 + 1)y] - y = √2 ⇔ -2y = 1 ⇔ y = -![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7B1%7D%7B2%7D)
Từ đó x = 1 - (√2 + 1)(-
) = ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7B3%20+%20%5Csqrt%7B2%7D%7D%7B2%7D)
Vậy hệ có nghiệm (x; y) = (
; -
)